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SUMMARY TECHNICAL REPORT 
OF THE 

NATIONAL DEFENSE RESEARCH COMMITTEE 


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States within the meaning of the Espionage Act, 50 U.S.C., 31 and 32, as 
amended. Its transmission or the revelation of its contents in any manner to 
an unauthorized person is prohibited by law. 

This volume is classified RESTRICTED in accordance with security regula- 
tions of the War and Navy Departments because certain chapters contain 
material which was RESTRICTED at the date of printing. Other chapters 
may have had a lower classification or none. The reader is advised to consult 
the War and Navy agencies listed on the reverse of this page for the current 
classification of any material. 



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publication by the Summary Reports Group of the Columbia 
University Division of War Research under contract OEMsr-1131 
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ume was printed and bound by the Columbia Lniversity Press. 

Distribution of the Summary Technical Report of NDRC has 
been made by the War and Navy Departments. Inquiries concern- 
ing the availability and distribution of the Summary Technical 
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Report of NDRC, has been written, edited, and printed under 
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revisions. 




SUMMARY TECHNICAL REPORT OF DIVISION 6, NDRC 


VOLUME 7 


PRINCIPLES AND APPLICATIONS 
OF UNDERWATER SOUND 


OFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT 
V ANNE VAR BUSH, DIRECTOR 


NATIONAL DEFENSE RESEARCH COMMITTEE 
JAMES B. CON ANT, CHAIRMAN 


DIVISION 6 
JOHN T. TATE, CHIEF 




NATIONAL DEFENSE RESEARCH COMMITTEE 


James B. Conant, Chairman 
Richard C. Tolman, Vice Chairman 
Roger Adams Army Representative 1 

Frank B. Jewett Navy Representative 2 

Karl T. Compton Commissioner of Patents 3 

Irvin Stewart, Executive Secretary 


l Army Representatives in order of service: 

Maj. Gen. G. V. Strong Col. L. A. Denson 

Maj. Gen. R. C. Moore Col. P. R. Faymonville 

Maj. Gen. C. C. Williams Brig. Gen. E. A. Regnier 

Brig. Gen. W. A. Wood, Jr. Col. M. M. Irvine 

Col. E. A. Routheau 


2 Navy Representatives in order of service: 

Rear Adm. H. G. Bowen Rear Adm. J. A. Furer 
Capt. Lybrand P. Smith Rear Adm. A. H. Van Keuren 
Commodore H. A. Schade 
3 Commissioners of Patents in order of Service: 

Conway P. Coe Casper W. Ooms 



NOTES ON THE ORGANIZATION OF NDRC 


The duties of the National Defense Research Committee 
were (1) to recommend to the Director of OSRD suitable 
projects and research programs on the instrumentalities of 
warfare, together with contract facilities for carrying out 
these projects and programs, and (2) to administer the tech- 
nical and scientific work of the contracts. More specifically, 
NDRC functioned by initiating research projects on requests 
from the Army or the Navy, or on requests from an allied 
government transmitted through the Liaison Office of OSRD, 
or on its own considered initiative as a result of the experi- 
ence of its members. Proposals prepared by the Division, 
Panel, or Committee for research contracts for performance 
of the work involved in such projects were first reviewed by 
NDRC, and if approved, recommended to the Director of 
OSRD. Upon approval of a proposal by the Director, a con- 
tract permitting maximum flexibility of scientific effort was 
arranged. The business aspects of the contract, including 
such matters as materials, clearances, vouchers, patents, 
priorities, legal matters, and administration of patent matters 
were handled by the Executive Secretary of OSRD. 

Originally NDRC administered its work through five 
divisions, each headed by one of the NDRC members. 
These were: 

Division A — Armor and Ordnance 

Division B— Bombs, Fuels, Gases, & Chemical Problems 
ij^on C — Communication and Transportation 
“ D — Detection, Controls, and Instruments 
3 — Patents and Inventions 


In a reorganization in the fall of 1942, twenty-three ad- 
ministrative divisions, panels, or committees were created, 
each with a chief selected on the basis of his outstanding 
work in the particular field. The NDRC members then be- 
came a reviewing and advisory group to the Director of 
OSRD. The final organization was as follows: 

Division 1 — Ballistic Research 

Division 2— Effects of Impact and Explosion 

Division 3 — Rocket Ordnance 

Division 4 — Ordnance Accessories 

Division 5 — New Missiles 

Division 6 — Sub-Surface Warfare 

Division 7 — Fire Control 

Division 8 — Explosives 

Division 9 — Chemistry 

Division 10 — Absorbents and Aerosols 

Division 11 — Chemical Engineering 

Division 12 — Transportation 

Division 13 — Electrical Communication 

Division 14 — Radar 

Division 15 — Radio Coordination 

Division 16 — Optics and Camouflage 

Division 17 — Physics 

Division 18— War Metallurgy 

Division 19 — Miscellaneous 

Applied Mathematics Panel 

Applied Psychology Panel 

Committee on Propagation 

Tropical Deterioration Administrative Committee 


library 


Con& rcSS 



490952 


2015 


NDRC FOREWORD 


A s events of the years preceding 1940 revealed 
u more and more clearly the seriousness of the 
world situation, many scientists in this country came 
to realize the need of organizing scientific research 
for service in a national emergency. Recommenda- 
tions which they made to the White House were 
given careful and sympathetic attention, and as a 
result the National Defense Research Committee 
[NDRC] was formed by Executive Order of the 
President in the summer of 1940. The members of 
NDRC, appointed by the President, were instructed 
to supplement the work of the Army and the Navy 
in the development of the instrumentalities of war. 
A year later, upon the establishment of the office of 
Scientific Research and Development [OSRD], 
NDRC became one of its units. 

The Summary Technical Report of NDRC is a 
conscientious effort on the part of NDRC to sum- 
marize and evaluate its work and to present it in a 
useful and permanent form. It comprises some 
seventy volumes broken into groups corresponding 
to the NDRC Divisions, Panels, and Committees. 

The Summary Technical Report of each Division, 
Panel, or Committee is an integral survey of the 
work of that group. The first volume of each group’s 
report contains a summary of the report, stating the 
problems presented and the philosophy of attacking 
them and summarizing the results of the research, 
development, and training activities undertaken. 
Some volumes may be “state of the art” treatises 
covering subjects to which various research groups 
have contributed information. Others may contain 
descriptions of devices developed in the laboratories. 
A master index of all these divisional, panel, and 
committee reports which together constitute the 
Summary Technical Report of NDRC is contained 
in a separate volume, which also includes the index 
of a microfilm record of pertinent technical labora- 
tory reports and reference material. 

Some of the NDRC-sponsored researches which 
had been declassified by the end of 1945 were of 
sufficient popular interest that it was found desirable 
to report them in the form of monographs, such as 
the series on radar by Division 14 and the monograph 
on sampling inspection by the Applied Mathematics 
Panel. Since the material treated in them is not 


duplicated in the Summary Technical Report of 
NDRC, the monographs are an important part of 
the story of these aspects of NDRC research. 

In contrast to the information on radar, which is 
of widespread interest and much of which is released 
to the public, the research on subsurface warfare is 
largely classified and is of general interest to a more 
restricted group. As a consequence, the report of 
Division 6 is found almost entirely in its Summary 
Technical Report, which runs to over twenty vol- 
umes. The extent of the work of a Division cannot 
therefore be judged solely by the number of volumes 
devoted to it in the Summary Technical Report of 
NDRC: account must be taken of the monographs 
and available reports published elsewhere. 

Any great cooperative endeavor must stand or fall 
with the will and integrity of the men engaged in 
it. This fact held true for NDRC from its inception, 
and for Division 6 under the leadership of Dr. John 
T. Tate. To Dr. Tate and the men who worked with 
him — some as members of Division 6, some as repre- 
sentatives of the Division’s contractors — belongs the 
sincere gratitude of the Nation for a difficult and 
often dangerous job well done. Their efforts con- 
tributed significantly to the outcome of our naval 
operations during the war and richly deserved the 
warm response they received from the Navy. In 
addition, their contributions to the knowledge of the 
ocean and to the art of oceanographic research will 
assuredly speed peacetime investigations in this field 
and bring rich benefits to all mankind. 

The Summary Technical Report of Division 6, 
prepared under the direction of the Division Chief 
and authorized by him for publication, not only 
presents the methods and results of widely varied 
research and development programs but is essentially 
a record of the unstinted loyal cooperation of able 
men linked in a common effort to contribute to the 
defense of their Nation. To them all we extend our 
deep appreciation. 



Vannevar Bush, Director 
Office of Scientific Research and 


J. B. CONANT, 
National Defense 




FOREWORD 


T he assured way of effecting improvement in any 
art is through a broadening of the base of funda- 
mental knowledge of all the factors upon which the 
art rests. In his statement to the Navy of the plan 
of organization and of the objectives of Division 6, 
Dr. F. B. Jewett emphasized this fact and recom- 
mended as a first objective “the most complete 
investigation possible of all the factors and phenom- 
ena involved in the accurate detection of submerged 
or partially submerged submarines and in antisub- 
marine devices.” In this statement he had partic- 
ularly in mind phenomena in the field of underwater 
sound. Consequently, Division 6 promptly extended 
and intensified the research program in the physics 
of underwater acoustics already begun under NDRC 
contract with the Woods Hole Oceanographic Insti- 
tution, and, in addition, assigned to their San Diego 
laboratory, organized under contract with the Uni- 
versity of California, a principal responsibility for 
the systematic study of all phases of underwater 
acoustics. All of the Division’s laboratories which 
were concerned with the development of underwater- 
sound equipment contributed much to these studies. 
In this connection special mention should be made 
of the Underwater Sound Reference Laboratories, 
whose development of basic standards of measure- 
ment and of methods of calibration of transducers 
(described in Volumes 10 and 11 of Division 6) was 
essential to the program. 

To coordinate and review the entire research pro- 
gram of the Division in the field of underwater 
acoustics, there was soon established in the head- 
quarters office of the Division a section of the Colum- 
bia University “Special Studies Group” which came 
to be known as the “Sonar Analysis Group.” The 
function of this group was to assist in the analysis of 
data being accumulated by Woods Hole, San Diego, 
and other laboratories, to assess their significance in 
relation to the development and design of sonar gear, 
and to present their conclusions to other groups in 
the NDRC and to groups in the Navy interested in 
such matters. Quite promptly the interest of the 
Navy led to its very active participation, in fact, to 
actual sharing in the operations of the Sonar Analy- 
sis Group. 

Because of their fundamental importance, the 
results of this research program have been rather 
completely summarized in four volumes (Volumes 
6A, 7, 8, and 9 of Division 6) of the Summary Report 


Series. Volume 6A, “Oceanography,” deals with the 
physical properties of the medium. Volume 7, the 
present one, may be regarded as a general text on 
underwater acoustics, while Volumes 8 and 9 deal 
with certain more specific aspects of the subject. 

The responsibility for preparing this report was 
undertaken by Dr. Carl Eckart, Associate Director 
of the San Diego Laboratory. In this he has had the 
assistance of a number of persons who have been in 
one way or another closely associated with this re- 
search program. The Division appreciates the efforts 
of those who have participated in the preparation of 
this report and particularly recognized its obligations 
to the Navy which made it possible for Dr. Eckart 
to prepare most of this material after responsibility 
for operating the San Diego Laboratory had been 
transferred to the Navy. 

The institutions principally involved in these 
researches have already been mentioned. For over 
four years it was peculiarly a group effort, and no 
attempt will be made to name the large number of 
individual scientists who contributed. The names of 
those who ably directed various groups sharing in 
this research program are Carl Eckart, C. O’D. 
Iselin, V. O. Knudsen, G. P. Harnwell, W. V. 
Houston, and Lyman Spitzer. Dr. H. Sverdrup, 
Director of the Scripps Institution, was appointed 
Consultant to the Division. He and his staff con- 
tributed significantly. 

As is true of the Division’s program as a whole, 
this research activity secured most effective support 
from the Navy, at first from Rear Admirals S. M. 
Robinson and A. H. Van Keuren, and later following 
changes in Navy assignments, from Vice-Admiral 
E. L. Cochrane and Rear Admiral J. A. Furer. More 
detailed and most helpful* liaison was provided by 
Captain Rawson Bennett, Jr., Commander Roger 
Revelle, Commander J. C. Myers and others in the 
Bureau of Ships and Commander Burwell of the 
Office of the Coordinator of Research and Develop- 
ment. In addition, the Sonar Analysis Group, in 
particular, maintained close contact with the Opera- 
tions Research Group in the Office of the Com- 
mander-in-Chief. This, supplementing other liaison, 
facilitated prompt application of research results to 
operations. 




















































' 










PREFACE 


I N 1940 the National Defense Research Committee 
appointed a Subcommittee on the Submarine 
Problem. One of the recommendations of this sub- 
committee was the establishment, at San Diego, of a 
laboratory responsible for “a broad research program 
covering the fundamentals of every aspect of the 
problem.” San Diego was chosen because of its prox- 
imity to deep water, and because of the number of 
days per year that would be favorable to research at 
sea. This recommendation resulted in the organiza- 
tion, in 1941, of such a laboratory by the University 
of California. It was located in the buildings of the 
U. S. Navy Radio and Sound Laboratory and became 
known as the University of California Division of 
War Research [UCDWR]. 

UCDWR continued its activities until July 1946, 
and received many additional assignments. Other 
NDRC organizations, notably the Columbia Uni- 
versity Division of War Research, the Sonar Analysis 
Group, and the Woods Hole Oceanographic Institu- 
tion, as well as various Naval shore activities, and 
vessels of the Fleet, also participated in the ‘‘ ‘broad 
research program.” The urgencies of World War II 
somewhat limited the broadness and thoroughness of 
this research, but a continually expanding subdivision 
of UCDWR — eventually known as the Sonar Data 
Division — was actively engaged in the accumulation 
of scientific data on underwater sound for nearly five 
years. When, in the normal course of reconversion, 
OSRD ceased to support this work, the Bureau of 
Ships assumed the contract. 

This Summary Technical Report attempts to cover 
the scientific work of all the above named organiza- 
tions. It was prepared by the Sonar Data Division 
of UCDWR, and, as this was the largest of the 
associated research groups, it is inevitable that its 
contributions occupy a large part of the report. An 
effort has been made to cover the field completely 
and to include the work of the other groups in ade- 
quate detail, but the editor is conscious that this 
ideal has not always been achieved. 

The operations of the Sonar Data Division were a 
good example of cooperative scientific effort. Many 
of the advantages of free individualistic research 
were unavoidably lost because of the necessity for 
concentrated attacks on constantly shifting objec- 
tives, but without exception each member of the staff 
contributed as generously to the group effort as he 
would have to his personal research. The normal 


desire for signed publications was cheerfully sacri- 
ficed to the anonymity of classified reports, so that, 
in retrospect, it is very difficult t<5 give due credit for 
individual achievement. The constantly changing 
assignments, and the number of people engaged in 
different phases of the same urgent problem, pre- 
vented the association of single names with most of 
the important conclusions. It is therefore essential 
to include in this preface a brief account of the staff 
of the Sonar Data Division of UCDWR. 

The first Director of UCDWR was Dr. V. O. 
Knudsen, who was assisted by Dr. K. S. Van Dyke, 
Mr. L. J. Sivian, and Dr. H. E. Hartig in organizing 
the work. During 1942, the three first named were 
transferred to other war activities, and the director- 
ship was assumed by Dr. G. P. Harnwell. The lab- 
oratory was divided into three major parts : the Sonar 
Training Division, led by Dr. Hartig; the Sonar 
Devices Division, led by Dr. F. N. D. Kurie, and 
the Sonar Data Division, led by the undersigned and 
later by Dr. R. H. Fleming. While all three divisions 
took some part in the broad research program, the 
Sonar Data Division had the primary responsibility 
for it. 

Some of the earliest experimental work was that 
on reverberation, under the leadership of Dr. C. F. 
Eyring. This group later expanded its activities under 
the joint leadership of Drs. R. J. Christensen and 
R. W. Raitt, to include the experiments on the trans- 
mission of 24-kc sound and on the properties of 
wakes. Other members of this group, who have made 
major contributions to the work reported in the 
present volume, are Messrs. R. R. Carhart, G. E. 
Duvall, T. H. Schafer, M. J. Sheehy. The onerous 
task of conducting the extensive experiments at sea 
was largely under the leadership of Messrs. N. Most 
and J. D. Frautschy. Dr. W. R. Rayton also did 
much work at sea, as well as in cooperation with 
Mr. R. C. Fisher in developing the periodmeter with 
which the records reproduced in Chapter 5 were 
obtained. 

Other early experimental work was on background 
noise and on the attenuation of sound, under the 
leadership of Mr. F. A. Everest, Dr. R. W. Young 
and Mr. H. T. O'Neil. Under the joint leadership of 
the first two, the activities of this group expanded 
to include all phases pf low-trequqney underwater 
sound. Major contributions to this phase of the work 
were made by Mefers. A. R. Champion, T. F. 



■\> 


X 


PREFACE 


Johnston, T. McMillian, L. Sepmeyer, and G. P. 
Welch. The first three spent much time at sea. 

The Oceanographic Section was organized in 1941 
under the direction of Dr. H. U. Sverdrup of Scripps 
Institution of Oceanography. Other members of that 
Institution joined UCDWR at the same time. This 
section was later headed by Dr. R. H. Fleming, who 
was assisted by Dr. R. D. Russell; the studies of 
bottom sediments were carried on under the direction 
of Drs. F. P. Shepard and K. O. Emery; the biolog- 
ical aspects of underwater noise were studied by 
Dr. M. W. Johnson; Mr. F. C. LaFond was in charge 
of the analysis of thermal data. The photographs of 
internal waves (Chapter 4) were made at the Uni- 
versity of Iowa by Mr. W. H. Munk of the Oceano- 
graphic Section, Professor Hunter Rouse, and Dr. 
J. S. McNown of the Iowa Institute of Research, 
University of Iowa. Later experiments on internal 
waves in the sea were performed by Dr. W. C. Ufford. 

The work on the propagation of explosive sound 
was planned by Dr. W. R. Smyth, and carried on 
under the leadership of Dr. R. A. Peterson, by Dr. 
B. G. Eaton, Mr. T. F. Johnston, and Dr. R. W. 
Raitt. 

Psycho-acoustic studies were carried on by Dr- 
A. M. Small, assisted by Mr. R. S. Gales, and Mr. 
L. J. Goldberg. The work of this group and other 
groups would have been impossible had it not been 
for the excellent recording facilities designed and 
largely constructed by Mr. L. Sepmeyer. These in- 
clude a radio link for making high-fidelity phono- 
graph recordings, in the shore laboratory, of under- 
water sounds picked up at sea. 

Other groups of the UCDWR staff made essential 
contributions by designing and constructing equip- 
ment, or by contributing services and facilities. These 
include the Transducer Design Group, the Calibra- 
tion Group, the Circuit Laboratory, the Marine 
Facilities Group, and the Photographic Laboratory. 

It is scarcely possible to make adequate acknowl- 
edgment of the numerous and varied contributions 
made by personnel of the U. S. Navy. The USS 
Jasper (PY C -13) was an essential part of the lab- 


oratory throughout its existence; it was later joined 
by the YP-267 ( ex-Democracy ) and YAG-6 (ex- 
Enchantress ) . The able and willing cooperation of the 
officers and men of these vessels, as well as of the 
civilian-manned E. W. Scripps, made possible the 
experiments at sea. For many experiments, the above 
vessels were joined by others, made available by 
various commands of the U. S. Fleet. Especially to 
be commended is the effective manner in which the 
officers of many of these visiting vessels responded 
to the strange and incomprehensible requests of the 
civilian scientists. The complex operations were 
greatly facilitated by the liaison officers, notably by 
Dr. Roger Revelle, Comdr. (USNR), stationed at 
the Bureau of Ships in Washington, and by Dr. L. P. 
Delsasso, Comdr. (USNR), stationed at San Diego. 

In preparing the manuscript of this report, the 
undersigned was ably assisted by Mr. C. E. Behrens. 
In most cases, first drafts of sections were written 
by those actively concerned in the original work. 
These drafts were then edited into a coherent whole, 
but it is feared that some degree of repetitiousness 
and incoherence remains. The line-drawings were 
prepared by Mrs. Florence Clarkson Welch and Miss 
Carolyn Wilhelm, and the photographic material, by 
Messrs. A. E. Handley and C. M. Johnson. 

Dr. Lyman Spitzer, Jr., and other members of the 
Sonar Analysis Group made the manuscripts of other 
Summary Technical Reports (Volumes 8 and 9) 
available in advance of publication. These were 
consulted freely in preparing many chapters. 

Portions of the final manuscript were read by Dr. 
Spitzer, Dr. Revelle, Dr. Edward Gerjuoy, and Mr. 
John Major, Lieut. (USNR), as well as by members 
of the Sonar Data Division. Their criticisms and 
suggestions have been most helpful. The Summary 
Reports Group of NDRC gave generous assistance 
on all matters relating to publication. 

The editor wishes to record his personal apprecia- 
tion of the cordial manner in which all of those 
named, and many others, extended their help to him. 

Carl Eckart 
Editor 


CONTENTS 





SOUND 


CHAPTER 

1 Theory of an Ideal Medium 

2 The Refraction of Sound 

3 The Transmission of Sound in the Sea 

4 The Oceanography of Sound Conditions 

5 Echoes, Scattering and Reverberation 

6 Wakes 


PAGE 



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PART II 
ECHO RANGING 

7 The Acoustic Output of Sonars ^ 135 

8 Target Strength and Echo Level 153 

9 Maximum Echo Ranges When Background Noise is 

Limiting 175 

10 Maximum Echo Ranges When Reverberation is 

Limiting 192 

1 1 Miscellaneous Echo Ranging Applications 200 


PART III 
LISTENING 

12 The Acoustic Output of Ships and Submarines . . . 223 

13 Background Noise 243 

14 Hearing and Recognition 255 

15 Sonic and Supersonic Listening 266 

List of Symbols Used 279 

Bibliography 281 

Contract Numbers 286 

Project Numbers 287 

Index 289 








PART I 

BASIC PRINCIPLES OF UNDERWATER SOUND 

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Chapter 1 


THEORY OF AN IDEAL MEDIUM 


i.i INTRODUCTION 

ill Objectives 

T he general purpose of this book is to discuss the 
factors that limit the performance of underwater 
sound apparatus. These can be divided into three 
groups, according to their cause. 

1. Those originating in the sea; 

2. Those originating in the electrical and mechani- 
cal parts of the gear; 

3. Those originating in the operator who uses the 
gear. 

The factors that originate in the sea itself are the 
principal subject matter of this book. 

It is assumed that the reader has had college courses 
in sound, electricity, and mathematics. While it will 
be helpful if the reader has a thorough knowledge of 
sound and acoustics, the discussion has everywhere 
been kept at as elementary a level as possible, with 
a minimum use of mathematics. One or more of the 
standard textbooks on sound should be available for 
reference (see bibliography). All these books deal 
with acoustic phenomena as they are observed in 
relatively confined regions, such as the air in a room 
or the water in a tank. In the open air and open 
sea, other phenomena become dominant and often 
obscure the simple relations that are observed in 
the laboratory. 

There are various reasons for this. Some effects in- 
crease with the distance to which the sound is propa- 
gated, while others remain relatively constant. The 
temperature differences in a small tank of water can 
be reduced by stirring to the point where they are 
negligible; in the ocean, temperature differences pro- 
duce large effects over long distances. Again, the water 
in a tank can be assumed not to move or change its 
temperature during an experiment; waves and ripples 
on the surface can be eliminated to a considerable 
extent. None of these simplifying conditions can be 
enforced in the sea, and the principal purpose of this 
book is to discuss the manner in which these dynamic 
properties of the ocean influence the propagation of 
sound and cause it to differ from propagation in an 
ideal static medium. 


However, in order to furnish a standard of com- 
parison, this first chapter will review the generation 
and transmission of sound in an ideal medium. 

1.2 LARGE AND SMALL SOURCES IN 
AN IDEAL MEDIUM 

i.2.i Intensity and Pressure Level 

When a body of any shape whatsoever vibrates har- 
monically in an ideal fluid of infinite extent, longitu- 
dinal waves are propagated outwards, and during the 
transmission of the waves the fluid is condensed and 
rarefied cyclically with the frequency of vibration. 
The root-mean-square (rms) departure from the aver- 
age hydrostatic pressure is called the sound pressure. 
The sound field is completely described if the sound 
pressure at every point is specified. In the case of 
simple sound fields the flow of sound energy at a given 
point can be calculated if the sound pressure only at 
that point is known. 

When points on the surface of the vibrating body 
move in a more complicated manner, so that the as- 
sumption of simple harmonic motion with a definite 
frequency cannot be made, the above remarks are in 
need of some modification. The motion of the medium 
at a given point is then a sort of delayed average of 
the motions of all the points on the vibrating object. 
The sound field is not completely specified unless this 
motion of the medium is given at each point. For some 
purposes, it is still sufficient to specify only the rms 
pressure; for others, additional information about the 
motion of the medium is required, but it is rarely nec- 
essary or possible to describe it completely. Usually 
it is sufficient to know how the sound energy is dis- 
tributed among the various frequencies of vibration — 
to know the “power spectrum” of the sound. 

Definitions of Intensity 

Intensity is defined in various ways: 

Energy Density (W). Energy density at a point is 
the quantity of energy in a unit volume of the medium 
about the point. In any sound field the energy density 
is given by 

W = —. (1) 

PC 2 


1 


2 


THEORY OF AN IDEAL MEDIUM 


where p = the rms sound pressure at the point, 
p = the density of the medium, and 
c = the velocity of sound in that medium. 

If p is measured in dynes/cm 2 , p in grams/cm 3 , and 
c in cm/sec, then W will be measured in ergs/cm 3 . 

Energy Flow (F). Energy flow at a point in the 
sound field is the quantity of energy passing in one 
second through a unit area containing the point and 
normal to the direction of the flow. The calculation of 
the energy flow is, in general, not simple. In the sim- 
plest unidirectional sound fields it is given by 

p 2 

F = t - = C W. (2) 

pc 

With p, p, and c measured in cgs units as before, 
energy flow F will be in ergs/ (sec) (cm 2 ). In some ap- 
plications of sound it is convenient to express the 
energy flow in watts/yd 2 rather than in cgs units; 
the pressure, however, is still measured in dynes per 
sq cm. Using the appropriate values for the density 
of sea water and the velocity of sound in the ocean, 
the energy flow in these units is given by 

F = (5.57 X 10 -9 )p 2 (watt/yd 2 ). (3) 

Intensity (7). For many practical purposes a third 
definition of sound intensity may be used, 

I = p 2 (dynes 2 /cm 4 ). (4) 

This unit is convenient because, while energy flow 
and energy are difficult to measure, the sound pres- 
sure p is easily measured. This definition of intensity 
will be used in this book. Where it becomes necessary 
to discuss the energy flow, this will be indicated 
explicitly. 

Sound Level (L) 

The values of p encountered in practice range from 
about 10~ 4 to 10 6 dynes/cm 2 , hence the decibel system 
is used to specify sound intensities. The pressure level 
of sound, or simply the sound level , L, in decibels, is 
defined by the equation 

L = 10 log I = 20 log p (db). (5) 

The logarithm is to the base 10. 

Other Units of Sound Intensity and Pressure 

Two units of pressure are in common use. These 
are 1 dyne/cm 2 and 0.0002 dyne/cm 2 . The latter unit 


is almost invariably used in dealing with airborne 
sound. Both units have been used in dealing with 
underwater sound, but the dyne/cm 2 is preferred by 
the Navy. However, it is sometimes necessary to con- 
vert from one system of units to the other. 

Let p and p f be the numbers expressing the same 
pressure in the two units. Then 

p dynes/cm 2 = p f (0.0002 dyne/cm 2 ) (6) 

or p f = 5,000p. 

In the same way, let L and 7/ be the levels in the 
two cases. Then 

7/ = 20 log p' = 20 log (5,000p), 

= 20 log p+ 74, 

= L+74. (7) 

In this book the dyne/cm 2 will be used only for 
underwater sound. In keeping with international 
practice, the unit 0.0002 dyne/cm 2 will be used for 
airborne sound. 

It is unfortunate that no name has been given this 
latter unit, so that it is necessary to use such cumber- 
some phrases as “pressure in units of 0.0002 dyne per 
square centimeter/ ’ and “the sound level in decibels 
above 0.0002 dyne per square centimeter.” To avoid 
such interruptions to the reader’s train of thought, 
the simpler phrases “pressure” and “sound level” 
will be used throughout ; unless specifically indicated 
in footnotes, the unit will be the dyne/cm 2 for under- 
water sound and 0.0002 dyne/cm 2 for airborne sound. 
The relation among the several units is shown 
graphically in Figure 1. 

1.2.2 Large and Small Sound Sources 

The character of the sound field is determined in 
the first instance by the source of the sound. In the 
ocean the sound sources that come into consideration 
differ widely. Hulls of ships are large sources emitting 
noise with a complicated spectrum; sound projectors 
are moderately large sources emitting relatively pure 
tones or sound of controlled frequency bands; minute 
air bubbles may be secondary sources of sound. It is 
important to characterize all of them. 

Any source can be considered to be divided into 
elemental areas, each of which acts as a point source 
of sound. If the linear dimensions of the source are 
small compared to the wavelength of the sound, the 
differences in the distances from a remote point in the 
sound field to any two elemental areas on the source 
are small compared to the wavelength, so that all 


LARGE AND SMALL SOURCES IN AN IDEAL MEDIUM 


3 


DB 

ABOVE 
DYNES . DYNE 
1 


L' 

DB 

ABOVE 

0.0002 

DYNE 


WATT WATT 


CM 2 CM 2 CM 2 YARDS 2 CM 2 


10 r 


I ATM 


I0 5 f 


I0 4 f 


10 


•.4 


120 T 


I00-- 


60 - 


10 - 60- 


10 - 40 - 


10 - 20 - 


I0” 1 -- -20 - 


I0’ 2 4- -40 1 


I0 _i - -60- 


180 - 


160 - 


140- 


120 - 


100 - 


80 

-74 


60 - 


40- 


20 - 


I0 4 t 


10 2 f 


10 ' 


1 - 2 - 


10- 1 0°[ -80 4- 


-5.6 


I0‘ l2 f I0"'°4 -160- 


10 


,-14 


io' 2 4- 


I f IO~ 4 4- -40 4- 


I0~ 6 - -60- 


-8 


io’ 6 - io' ,0 -|- -loo 


0.6 4 


tO -10 - | 0 - ,4 1 -|40 


s -16 


DB 

ABOVE 
^ WATT 

CM 2 

Ot 


- 20 - 


- 122 - 


-18 

10 - -180 


0 l0 ’ l6j - IO' 20 -!- -200 

-80- 1 * 

Figure 1. Comparison of units for underwater sound. 


4 


THEORY OF AN IDEAL MEDIUM 


pressures arrive at the remote point substantially at 
the same time; the delayed average mentioned above 
is then a simple sum and the pressures from each of 
the elementary areas add. The sound, moreover, is 
radiated uniformly in all directions. In this case the 
source can be called small. 

If a source of simple harmonic waves is large com- 
pared to one wavelength, the waves from the various 
elementary areas will not all arrive at a given point 
at the same time. Hence there will be interference 
effects, and the intensity radiated in some directions 
will be greater than in others. 

If the source is large, for example a ship, but emits 
noise rather than single frequency sound, the more 
obvious interference effects largely disappear. How- 
ever, the intensity radiated in some directions will 
still be different from that in others. In this case, 
complications in measurement can occur because 
some parts of the source are nearer the point of meas- 
urement than others. Usually these complications 
disappear when the distance to the nearest point of 
the source is more than four or five times its largest 
dimension. 


1.2.3 The Inverse Square Law — Small 
Sources 


If a very small radially pulsating sphere is imagined 
placed in the medium, its pulsations spread out spheri- 
cally and affect the whole space occupied by the 
medium. The power (total energy per second) trans- 
mitted through any concentric spherical surface is 
constant, and since the surface area is 47rr 2 , where r 
is the distance (in yards) of the wave front from the 
source, the energy flow can be expressed by the 
equation 


F = 


P 

(4tt r 2 )’ 


(8) 


where F is the energy flow in watts/yd 2 at a distance 
r from the source and P the total power radiated by 
the source. This can also be expressed in terms of the 
intensity as follows. 

Equations (3) and (4) apply in this simple case, 
and thus 

F = (5.57 X 10 9 )p 2 = 5.57 X 10 9 / 

“7TS (watts/ yd 2 ). (9) 


Define Ii so that 


(5.57 X 10 9 )/i =7-, 

4tt 

(10) 

_ h 

/=— , 

( 11 ) 


and 1 1 can also be defined as the intensity at a point 
1 yd from the center of the sphered 
In the decibel system, equation (11) becomes 

L = Li — 20 log r, (12) 

where L = 10 log I is the sound level at range r and 
Li = 10 log 7i is the level at unit range. The quantity 
Li is called the source level. 

Since graphical methods of presenting data are 
commonly used, it is important to become familiar 
with the appearance of the foregoing equations when 



Figure 2. Graph of I /I i as a function of range. 
Ordinates are the relative intensity; abscissas are 
the range in yards. 


they are plotted in different ways. The inverse square 
law, equations (11) and (12), can be presented graphi- 
cally in various ways. In Figure 2 the abscissa is pro- 
portional to r, and the ordinate is I //i( = 1 /r 2 ). This 
mode of presentation is not useful because the graph 
approaches too closely to the horizontal axis to be 
visible beyond about 10 yards. 

This objection is overcome by plotting 


L — Li = 10 log 



— 20 log r 


(13) 


as ordinate against r as abscissa. Such a graph is 
shown in Figure 3 ; the expansion of the scale for small 
values of I/I x into large negative values of L—L x 

a Equation (11) can also be expressed by the equation 
pr = const 

and is sometimes called the PD law (P for pressure, D for 
distance). 



LARGE AND SMALL SOURCES IN AN IDEAL MEDIUM 


RANGE, YD 



Figure 3. Graph of L-L i as a function of range. 
Ordinates are sound level, in decibels, above the 
source level; abscissas are range in yards. 

makes such a graph useful over a wider interval of 
ranges. 

A third type of graph also uses L — Li as ordinate, 
but plots log r instead of r as abscissa. Figure 4 is the 
graph of equation (12) plotted in this way. This has 


RANGE, YD, LOGARITHMIC SCALE 



Figure 4. Graph of L-Li as a function of range, the 
range being plotted on a logarithmic scale. 


two advantages: a much greater interval of ranges 
can be presented, and the graph of the inverse square 
law is a straight line. 


i. 2.4 The Inverse Square Law — Large 
Sources 

A large source does not radiate sound energy equally 
in all directions ; however, the intensity ratios at two 
remote points on a straight line through the source 
can still be calculated from the inverse square law. 
We may say that a large source is equivalent to an 
imaginary small source which radiates the same in- 


tensity in a given direction as the large source. If in 
equation (9) I\ were given a different value for each 
direction, this equation would still hold for large 
sources at great distances. This is not true for points 
close to the source. Figure 5 illustrates this schemati- 
cally. The solid graph represents the actual sound 


-t- 



Figure 5. Schematic diagram illustrating departures 
from inverse square law with a large source. The hydro- 
phone is supposed to have been carried along the line 
AB, and the solid graph shows the sound level that 
might have been observed. The dotted graph of the 
inverse square law shows that, at long ranges, the 
observed level is the same as would have been pro- 
duced by an imaginary small source at the center of 
the ship. The actual level nowhere reaches the value 
L\ and cannot, in the nature of things, be extended 
inside the ship. 


level in decibels along the line AB, while the dotted 
graph is the curve of equation (12). At great distances 
the two graphs coincide very closely; at short dis- 
tances marked departures occur. 


1.2.5 Directivity and Beam Patterns 

Instead of assigning a different value to the source 
intensity for each direction, one can designate the in- 
tensity at 1 yd in an arbitrary direction as the source 
intensity. The intensity in any other direction can 
then be obtained by multiplying by an appropriate 



6 


THEORY OF AN IDEAL MEDIUM 


50 ° 40 ° 30 ° 



Figure 6. Beam pattern of a projector. Radius repre- 
sents the value of 6. Note the difficulty of showing the 
side lobes. 


factor determined by the direction. In the case of a 
projector that concentrates most of its sound energy 
in a beam, the value of the intensity at 1 yd from the 
source in the direction of the axis of the beam is con- 
sidered to be the source intensity. Call it I a and let 
the intensity at 1 yd from the source in a direction 
making an angle 0 with the axis of the beam be /i(0), 
and the ratio of the latter to I a be 6(0), i.e., 


m= 


W) 

la ’ 


then equation (11) becomes 

IMS) 

r 2 


(14) 


(15) 


In converting to the decibel system, let L a = 10 
log I a’, L a is called the axial source level. Since 6(0) is 
usually a proper fraction, its logarithm is usually 
negative and represents a reduction in sound level. 
To avoid confusion in the use of signs, it is better to 
express this reduction as a positive number and sub- 
tract it than to add it as a negative number. It is 
therefore defined as B = — 10 log 6(0), and thus 
equation (15) converted to decibels becomes 

L = L a — B — 20 log r. (16) 

The quantity B is called the beam pattern or di- 
rectivity function and, by converting equation (14) to 
decibels, is defined by 

B = L a — Li. (17) 

It will be found useful in many equations. Equation 
(16) is convenient because L a is a constant, B de- 
pends on direction but not on range, and the term 20 


50 ° 40 ® 30 ° 



Figure 7. Beam pattern of Figure 6, with the ratio of 
I\(0)/I a expressed in decibels. M is the main “lobe”; 
the side lobes are marked 1 and 2. The dotted curves 
show the result of lobe suppression. 

log r depends only on range. At all points on the axis 
B = 0, since 6(0) is unity. 

Figures 6 and 7 show polar graphs of the functions 
6(0) and B(6) for the same projector. They have 
been calculated theoretically for a vibrating rect- 
angular plate, the side of which is about four wave- 
lengths long. Figure 6, the graph of 6, shows clearly 
that most of the sound is projected in directions which 
make angles less than 10° with the perpendicular to 
the plate. However, the very weak radiation at greater 
angles is of importance in some cases. Consequently, 
the graph of B (Figure 7) is useful, since the decibel 
scale emphasizes these small intensities. 

The maxima M, 1, 2, and others not shown are 
usually called “ lobes.” M is the main lobe. In order 
that sonar bearings be accurate, it is desirable to have 
the main lobe narrow. The side lobes 1 and 2 are, for 
many purposes, detrimental, and the design of mod- 
ern projectors lays emphasis on their suppression. 
With modern designs, the maxima of all side lobes are 
usually more than 20 db below that on the main lobe. 

Graphs like these are drawn for projectors from 
actual measurements of sound level in different di- 
rections. They are called “directivity patterns.” 

l.s ACTUAL MEDIUM: TRANSMISSION 
LOSS AND TRANSMISSION ANOMALY 

i.3.i The Ocean Is Not an Ideal 
Acoustic Medium 

The ocean, considered as a medium for the trans- 
mission of sound, is far different from the ideal one 



TRANSMISSION LOSS AND TRANSMISSION ANOMALY 


7 


RANGE, YD 



Figure 8. Graphs of equation H = B + 20 log r. Sketch at upper right shows applicability of the equation to echo ranging. 


presupposed in the previous section. It is not infinite 
in extent, being bounded by the bottom and the sur- 
face. It is not homogeneous; the upper layers are 
usually warmer than the lower ones and near large 
rivers may be less saline. For both reasons the water 
will be less dense in the upper layers. The tempera- 
ture and salinity may change also in a horizontal 
direction. Thus a sound wave propagated through 
the ocean will be distorted from the spherical shape 
characteristic of a small source in an ideal medium. 

Other less obvious acoustic properties of the ocean 
contribute to making the calculation of sound inten- 
sity difficult. As a sound wave travels outward from a 
source in the sea, some of the energy is converted into 
heat by friction because of the viscosity of the water. 
This process is called absorption. Another portion of 
the energy goes into the production of secondary 
wavelets which travel in directions other than that of 
the primary wave. This is the phenomenon called 
scattering. A more general term, embracing both ab- 
sorption and scattering, is attenuation. 

Even such a brief resume of the acoustic charac- 
teristics of the ocean indicates that the transmission 
of sound through it is a very complex process and 
that an experimental study of the individual aspects 
of the process is difficult. But it is possible to measure 
the total transmission loss and to observe how it 
deviates from the inverse square loss, equation (12), 
of the ideal medium. Experiments have been carried 
out in which one ship carries a sound projector and a 
second ship a hydrophone that receives the trans- 


mitted sound and measures its sound level. The study 
of these measurements has led to some useful con- 
clusions. 

1 . 3.2 Transmission Loss 

In these experiments the axial source level L a is 
kept constant and the sound level L is measured at 
the receiving ship. Usually the source ship is in mo- 
tion and the receiver stationary. The distance r 
between the two vessels can be measured by noting 
the difference in arrival time of the sound and a 
simultaneously emitted radio signal. 

The difference 

H = L a — L (18) 

is the loss in intensity level suffered by the sound in 
being transmitted from one ship to the other and is 
usually called the transmission loss. Except for sign, 
this is the same quantity as that plotted in Figures 
3 and 4. 

In the ideal medium assumed in Section 1.2, the 
transmission loss at a point on the axis of the beam 
would be 20 log r; at points not on the axis, H would 
be equal to B+ 20 logr, according to equation (16). 
Figure 8 shows graphs of H = B+2ti log r, the values 
of B having been taken from Figure 7. The sketch at 
the upper right shows the applicability of the results 
to echo ranging. A surface vessel is presumed to be 
ranging for possible targets at a depth d beneath the 
sound projector. The strength of the echo received 



8 


THEORY OF AN IDEAL MEDIUM 


RANGE, YD 



Figure 9. Comparison of transmission loss observed 
in an experiment with that calculated from the inverse 
square law. 


depends on the sound level which reaches the target 
and this decreases as the transmission loss H in- 
creases. Because the target is submerged beneath the 
projector, only that sound will reach it which is emit- 
ted at an angle 6 with the axis of the projector. As the 
surface vessel runs in on the target, this angle will 
increase, causing B to change. 

If the depth of the target were d = 0, d and B would 
be zero at all ranges. Consequently, the transmission 
loss H would be simply 20 log r. This is plotted as 
curve A. Curves B and C are plotted for the cases 
d = 60 and 300 ft, respectively. The minima of trans- 
mission loss are caused by the lobes of the beam 
pattern of Figure 7. These minima all have the same 
value in decibels for the case illustrated in the dia- 
gram; with lobe suppression, the minima at short 
range, i.e., large values of 0, are less pronounced and 
occur at larger values of H than those at longer 
ranges. They are shown by the dotted curve for 
d = 300 ft. 

1.3.3 Transmission Anomaly 

Experiment shows that equation (16) does not 
accurately represent the actual transmission loss. The 
difference between the observed value of II and that 
calculated from equation (16) is thus a measure of 
the departure of the ocean from an ideal medium; 
this departure might be called the transmission 
anomaly. 

It is sometimes difficult to isolate the effects of the 
beam pattern from the other causes of the transmis- 
sion loss ; consequently, a more practicable definition 
of transmission anomaly is the difference between the 
observed transmission loss and the transmission loss 



Figure 10. The same experimental data as Figure 9, 
plotted as transmission anomaly. 


calculated from the inverse square law alone without 
taking into account the directivity effect; the latter 
is thus included in the transmission anomaly de- 
fined by 

A = H — 20 log r; (19) 

whence the sound level can be calculated from the 
equation 

L = L a — A — 20 log r. (20) 

The usefulness of this concept of transmission 
anomaly is illustrated by Figures 9 and 10. These are 
based on experimental data obtained under special 
conditions. The solid curve of Figure 9 is a graph of 
observed transmission loss H and for comparison, the 
transmission loss calculated from the inverse square 
law is also plotted as a dotted curve. The difference 
between the two does not seem very great, and would 
hardly be noticed if the dotted curve were omitted. 
Yet the difference is very important in echo ranging. 
Thus, suppose the echo from a certain submarine can 
just be detected by a certain sonar when the trans- 
mission loss is 70 db. If the inverse square law were 
valid, it could then be detected at 3,000 yd, but 
under the actual transmission conditions it could not 
be detected beyond 1,250 yd, unless some other 
factor happened to be especially favorable at moder- 
ate ranges. Thus a graph like Figure 9 does not suf- 
ficiently emphasize the importance of relatively small 
departures from the inverse square law. 

On a graph like Figure 10, the graph of the inverse 
square law can be omitted, since it coincides with the 
horizontal axis at the top of the graph. The increasing 
departure from the inverse square law, as range in- 
creases, is immediately apparent. Moreover, a very 
simple law is also obvious : the transmission anomaly 
is proportional to range. This law is not valid under 



TRANSMISSION LOSS AND TRANSMISSION ANOMALY 


9 


all conditions; it will be discussed in detail in 
Chapter 3. When it is valid, one may express the 
transmission anomaly by the simple equation 

A = ar. (21) 

The coefficient a, is called the attenuation coefficient. 
In the example, it has the value 6 X 10 -3 db/yd. 

1 . 3.4 Causes of Transmission Anomaly 

Defined in this way, it is seen that the transmis- 
sion anomaly measures the difference in the trans- 
mission loss of sound from an actual source in the 
ocean and that of sound transmitted to the same 
range by a small source in an ideal medium. It may 
be helpful to summarize the components of the trans- 
mission anomaly: 


1. The effect of directivity , discussed in Section 1.2. 

2. Variations in temperature and salinity cause 
changes in density; together with increasing hydro- 
static pressure with depth these result in variation 
of the velocity of the sound and consequent refraction 
of the sound rays. This is discussed in the following 
chapter. 

3. The conversion of sound energy into heat energy, 
due to the viscosity of the water, called absorption. 

4. The scattering of sound by the surface, the bot- 
tom, and by obstacles in the body of the sea. It is 
advisable to distinguish between specular reflection, 
as from the surface and the bottom, and the diffuse 
reflections ordinarily designated by the term scat- 
tering. This is discussed in Chapter 5. 

5. Other factors about which little is known may 
contribute to the transmission anomaly. 


Chapter 2 

THE REFRACTION OF SOUND 


2.1 THE VELOCITY OF SOUND IN THE SEA 

2.1.1 Refraction of Sound Rays 

I N section 1.3 the refraction of sound in the sea 
was mentioned as a contributing cause of the 
transmission anomaly. In a homogeneous medium, 
sound would travel in straight lines. As in the ana- 
logous case of light, sound rays are curved if the 
velocity of propagation is not the same at all points. 
If a plane wave passes obliquely from a medium of 
lower to one of higher velocity, one part of the wave 
will travel faster than the other and the ray will be 
bent toward the medium of lower velocity. The ordi- 
nary laws of geometrical optics can be applied to the 
refraction of sound, although they are strictly true 
only for sound of very high frequency, and ignore 
such phenomena as scattering, diffraction, reflection, 
and absorption. These cannot always be ignored, but 
it is simplest to omit them from a first discussion. 

According to ray theory, the power transmitted in 
a beam bounded by a tube of adjacent rays will then 
remain constant, but if the beam is bent the varia- 
tion in the intensity, i.e., in the amount of power 
transmitted through a unit area, may be different 
from the variation that would occur if the rays re- 
mained straight. (See Figure 16A, B, C.) In order to 
calculate intensity, it is necessary, among other 
things, to know the shape of the sound rays and this 
in turn can be calculated from a graph of velocity of 
sound at different points. 

It should be said immediately that this ray theory 
does not agree in all respects with experiments on the 
transmission of sound. The agreement is close enough, 
however, to make an acquaintance with the theory 
essential to an understanding of the principles that 
have been deduced from the experiments. 

2.1.2 Influence of Temperature, Salinity, 
and Pressure on the Velocity of Sound 

The velocity of a sound at a given point in any 
medium is determined by the pressure and the den- 
sity of the medium at that point. In the ocean, the 
pressure increases with depth, and the density will 


vary if the temperature and salinity change. Of these 
three factors, temperature is by far the most im- 
portant in affecting the velocity of sound. 

Standard conditions of temperature, pressure, and 
salinity are conventionally chosen as 32°F, one at- 
mosphere pressure, and a saline content of 35 g/kg of 
sea water. Under these conditions, sound travels 
with a speed of 4,742.4 ft/sec, or about 1.44 X10 5 
cm/sec. 

The velocity increases with the temperature at a 
variable rate; Figure 1 shows the variation with 
temperature for various salinities. Changes of 20°F, 

TEMPERATURE, F 



Figure 1. Variation of the velocity of sound in the 
sea with temperature and depth. The symbol 0/00 
represents parts per thousand. 

in the upper layer of the ocean are not uncommon. 
An increase in salinity of one part in a thousand in- 
creases the velocity of sound 4.27 ft/sec; but salinity 
is comparatively constant except at the mouths of 
large rivers and thus in most cases its effect can be 
neglected. 

Increase of pressure with depth causes an increase 
in the speed of sound of 1.82 ft/sec per 100 ft of 
depth. It is obvious that the pressure effect will be 
important only if both the temperature and the salin- 
ity are constant. This is illustrated in Figure 4B, in 
which the solid line shows how the temperature varies 
with depth in a particular case and the dotted line 
indicates the change in the velocity of sound with 
depth corresponding to this temperature distribu- 
tion. The salinity effect is negligible. The effect of 


10 



THE VELOCITY OF SOUND IN THE SEA 


11 


pressure on the velocity of sound is evident in the 
upper 180 ft: while in this layer the temperature is 
constant, the velocity graph shows a slight increase 
in the velocity -with depth. Elsewhere the velocity 
curve is seen to parallel the temperature curve quite 
closely. 

At greater depths, temperature and salinity change 
only slightly, and the pressure effect dominates. The 
average temperature decreases with depth, la as 
shown in Figure 2, and down to a depth of about 
2,500 ft this decrease is sufficiently great to neu- 
tralize the effect of the increasing salinity and pres- 


TEMPERATURE, F SOUND VELOCITY, FT/SEC 
60 4850 5000 


|- 4000 


A — 


/ 

y 

* 

A 

/ 

I 

\ 

1 

\ 


1 

• 

/ 

TEMPERATURE 

i 

SALINITY 

1 


1 

• 



1 

' 






■ 

■ 

■ 

/ 

■ 

/ 

f 



1 

\ 

\ 



\ 

\ 



\ 

■ 

\ 

\ 



■ 

\ 



33 34 35 

SALINITY, °/oo 

Figure 2. Variation of temperature, salinity, and 
sound velocity with depth in the ocean. 


sure, so that the velocity of sound also decreases. At 
greater depths, the pressure effect begins to out- 
weigh the temperature effect, and the sound velocity 
is seen to increase with depth. This minimum velocity 
at great depths has interesting acoustic consequences 
and will be mentioned again. (See Section 2.3.3.) 


2 . 1.3 The Bathythermograph 

The temperature of the sea is measured with spe- 
cially constructed thermometers, with thermopiles, 
and with bathythermographs. The last mentioned is 
generally preferred: it is rugged and of convenient 
size, and can be used while the vessel is underway. 
Moreover, the bathythermograph draws a graph 
showing the temperature as a function of depth and 


does this automatically as it is lowered from a vessel. 
Thermometers are less convenient, since they usually 
show only the temperature at the greatest depth to 
which they were lowered. 

The construction of the bathythermograph is shown 
in Figure 3. As the instrument is lowered, a stylus is 
moved by the thermal expansion or contraction of a 


DEPTH 



THERMAL PRESSURE 

ELEMENT ELEMENT 


Figure 3. Construction of the bathythermograph. 

liquid in the copper thermometer tube. The increas- 
ing hydrostatic pressure compresses a bellows, which 
draws a smoked slide horizontally while the tempera- 
ture stylus moves in a vertical arc. The temperature 



TEMPERATURE, F 

50 ° 55 ° 60 ° 



Figure 4. {Top) Typical bathythermograph slide 
with coordinate grid superposed; ( bottom ) the cor- 
responding temperature-depth graph of the slide 
(solid curve), with the velocity of sound corresponding 
to this distribution (dotted curve). 


12 


THE REFRACTION OF SOUND 


and depth are thus recorded simultaneously on the 
slide. Figure 4A shows a typical slide with a coordi- 
nate grid superposed ; Figure 4B is the temperature- 
depth graph made from the trace on the slide. The 
graph of the velocity corresponding to this particular 
temperature-depth distribution has been referred to 
above. Such temperature-depth graphs are called 
bathythermograms. 


2.1.4 Horizontal and Vertical 

Temperature Changes 

In considering the refraction of sound in the sea, 
it can often be assumed that only the variation of 
temperature in a vertical direction is significant. This 
is equivalent to considering the ocean as consisting of 
strata, in any one of which the same temperature 
exists over a large horizontal distance. Compared 
with the vertical variation of temperature, the hori- 
zontal variations actually observed are very small. 2 
Changes in temperature over a horizontal distance of 
100 ft are rarely as much as 0.5°F, and usually less 
than 0.1°F. They also are not systematic. Over a 
vertical distance of 100 ft the temperature may vary 
as much as 10°F, as Figure 4 shows. This has been 
established in various ways. Simultaneous bathy- 
thermograph lowerings have been made from two 
ships separated by several thousand yards. The two 
traces were similar, but significant quantitative dif- 
ferences were observed. Even when lowerings are 
made simultaneously from the bow and stern of the 
same ship, the traces are not identical. Recording 
thermometers have been mounted on a submarine, 
and their records show quite conclusively that there 
are horizontal temperature differences over distances 
as small as 10 yd. The magnitude of these differences 
increases with distance but not in a systematic manner. 


2.1.5 Terminology for the Description of 
B a thy thermograms 


temperature, f temperature, f 





A ISOTHERMAL SURFACE LAYER 

TEMPERATURE. "F TEMPERATURE. F 




B NEGATIVE TEMPERATURE GRADIENT IN SURFACE LAYER 


TEMPERATURE. F TEMPERATURE. F 



Figure 5. Typical bathythermograms corresponding 
to various gradients. 


General Terms 

Twelve typical bathythermograms are exhibited 
in Figure 5. These illustrate the variable character of 
the temperature distribution in the surface layers of 
the sea. This diversity makes it difficult to develop a 
terminology for describing the temperature condi- 
tions near the surface. Certain oceanographic terms 
have been adopted, and in the analysis of sound trans- 


mission data (Chapter 3) specialized systems have 
been used for describing the general characteristics of 
the temperature-depth distribution. These will be 
discussed presently. 

All these systems distinguish sharply between tem- 
perature differences and temperature gradients, al- 
though this distinction is sometimes obscured in 
conversation. The temperature difference is obviously 


THE VELOCITY OF SOUND IN THE SEA 


13 


the difference between the temperature at two points 
and is measured in degrees Fahrenheit. The vertical 
temperature gradient is the rate at which the temper- 
ature changes with depth and is measured in degrees 
Fahrenheit per foot. It is also the slope of the trace 
on the bathy thermogram. 

Examination of Figure 5 shows that the temperature 
depth curve can usually be subdivided into segments 
having different temperature gradients. Negative 
gradients describe conditions in a layer where the 
temperature decreases with increasing depth, positive 
gradients describe layers in which the temperature 
increases with depth. The term isothermal is applied 
to layers in which the temperature is uniform. A 
layer where the temperature decreases very rapidly, 
particularly if it is immediately beneath an isother- 
mal layer or a layer of smaller gradient, is commonly 
called a thermocline. It is sometimes convenient to 
use the term permanent thermocline to describe the 
decrease in temperature (Section 2.1.2) which always 
occurs at great depths. 


If the temperature at any depth is greater than the 
temperature at some smaller depth, the symbol is 
POS. 

The surface temperature T is coded by taking 
T 7 / 10 to the nearest whole number. 

The symbol for any bathythermograph slide is a 
numeral consisting, in general, of six digits and a 
decimal point, e.g., 12345.6. Reading from left to 
right, the first digit is the code for D h the second for 
D 2 , etc. The digit to the right of the decimal point is 
the code for T. 

As examples of the code system, the upper right- 
hand bathy thermogram of Figure 5, showing an iso- 
thermal layer, has the code symbol 34445.7 ; the one 
immediately below it, 77777.8. The two bathyther- 
mograms on the left have code symbols 01359.5 and 
00023.7, top and bottom respectively. 

2.1.6 Direct Measurement of 

Sound Velocity 


A Code for Describing Temperature Differ- 
ences NEAR THE SURFACE OF THE SEA 


Instead of measuring the temperature, it is possi- 
ble to measure the velocity of sound directly with an 


As mentioned above, specialized systems have been 
devised for describing the general characteristics of 
the temperature distribution in the sea. One such 
system, used at San Diego, is a code constructed as 
follows: Let T = the temperature at the surface and 
D = the depth at which some specified temperature 
decrease occurs according to the following tabulation. 

Di = depth at which the temperature is T — 0.1 °F. 

D-> = depth at which the temperature is T — 0.3°F. 

D z = depth at which the temperature is T — 1.0°F. 

Di = depth at which the temperature is T — 5.0°F. 

D 5 = depth at which the temperature is T — 10.0°F. 


The bathythermogram is then described adequately 
for some purposes by the five depths, D h D 2 , D s , 
and D b . 

In order to enable the use of single digits for the 
respective values of the D’s the following code num- 
bers are used: 


Code digit 0: 
Code digit 1 : 
Code digit 2 : 
Code digit 3 : 
Code digit 4: 
Code digit 5 : 
Code digit 6: 
Code digit 7 : 
Code digit 8 : 
Code digit 9: 


0 

ft 

< 

D 

< 

5 

ft. 

5 

ft 

< 

D 

< 

10 

ft. 

10 

ft 

< 

D 

< 

20 

ft. 

20 

ft 

< 

D 

< 

40 

ft. 

40 

ft 

< 

D 

< 

80 

ft. 

80 

ft 

< 

D 

< 

160 

ft. 

160 

ft 

< 

D 

< 

320 

ft. 

320 

ft 

< 

D. 





Unassigned. 

D > greatest depth reached by the 
bathythermograph. 



Figure 6. Records of bathythermograph and velocity 
meter taken simultaneously. The two instruments 
were lashed together and lowered at the same time. 


instrument developed by the U.S. Navy Radio and 
Sound Laboratory [USNRSL]. 3 This device essen- 
tially measures the time required for sound to travel 


14 


THE REFRACTION OF SOUND 


from a projector to a hydrophone rigidly mounted 
about a foot away. It can be lowered into the sea on 
a cable through which it is also supplied with power. 

This velocity meter is sensitive to small changes 
in the velocity of sound occurring in a few feet, which 
the bathythermograph fails to detect because of the 
time lag in its thermometer. An example of the record 
of a velocity meter is shown in Figure 6, together 
with the record obtained from a bathythermograph 
which was lashed to it and lowered on the same line. 
The two records agree within the limits of experimen- 
tal error; both instruments contribute to this error. 


2 2 RAY THEORY 

2 . 2.1 Snell’s Law of Refraction 

The velocity of sound at each point in the sea being 
known, it is theoretically possible to calculate the 
sound rays, or paths, along which the sound travels. 
If the simplifying assumption can be made that the 
ocean is stratified, so that the temperature at all 
points having the same depth is the same, the calcu- 
lation becomes quite simple. 

Detailed explanations of the computational meth- 
ods are contained in several reports, 4 5 and only a 
summary of the method will be presented here. It is 
based on Snell’s law a , which is illustrated by Figure 
7, for an especially simple case of three layers or 


The ray in each layer is a segment of a straight 
line; but if the layers are imagined to become thinner, 
the ray approaches a smooth curve. However, at each 
point along the ray the relation between the inclina- 
tion of the ray and the velocity of sound is still given 
by equation (1). 


222 Rays in a Constant Gradient 

A somewhat less simple case is that of a constant 
gradient, which is illustrated in Figure 8. The gradient 
cannot remain constant indefinitely, since if it did, 
and the medium were of infinite extent, the sound 
velocity would ultimately become zero or negative, 
which is impossible. However, the depth at which 
the velocity would become zero is a convenient 
geometrical fiction and is used in constructing 
Figure 8. 


C SOUND VELOCITY 



/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

. FICTITIOUS ZERO LEVEL 



VELOCITY . RANGE 



Figure 7 . Diagram illustrating Snell’s law. Fi/cos 
0i = F 2 /cos d 2 = F 3 /cos 0 3 . 

strata, in each of which the sound velocity is con- 
stant. Consider a plane wave passing through these 
three layers; then Snell’s law is 

V1 V2 Vs 

COS 61 COS 62 COS 63 ^ 

where V\ and are the velocity and inclination of 
the ray in the first layer, and so on. 

* Snell’s law of refraction is discussed in all textbooks of 
physics as it applies to light rays. It is applicable, without 
change, to sound rays. 6 * 


Figure 8. Diagram illustrating the curvature of rays 
in a medium of constant velocity gradient. 

It can be shown that where the velocity gradient is 
constant the rays are circular. All these circles do not 
have the same radius but all their centers are at the 
fictitious level mentioned above. In the case of posi- 
tive gradients, this level is above the ray, which con- 
sequently curves upward. With negative gradients, 
the zero level is below the ray, and it curves down- 
ward as in Figure 8. The figure shows clearly that the 
radius of curvature of the ray depends on the angle 
at which it leaves the source. It should be noted that 
all rays leaving the source at steep angles have large 
radii, i.e., small curvature. Thus refraction has little 
effect on steeply inclined rays. 

In actual cases the curvature of all rays is small 
and their radii are correspondingly large. Consider, 
for example, the isothermal layer shown in Figure 4. 
In this layer the velocity increases with depth as a 
result of the increase in pressure; the gradient is 


TYPICAL RAY DIAGRAMS 


15 


a =0.182 ft/sec/ft increase in depth. Following 
through the discussion given above, it can be shown 
that the radii are all greater than 270,000 ft. This is 
equivalent to saying that a ray starting in a horizontal 
direction from a projector located in this layer will 
be bent upward 51 ft in traversing 1 mile in a hori- 
zontal direction. 

To illustrate the bending of a ray in a layer with a 
negative velocity gradient, consider the layer extend- 
ing from 180 to 230 ft in Figure 4B. It is seen that 
in this 50-ft layer the temperature decreases 8°F; 
the sound is passing through a region of negative 
gradient and consequently the ray is bent downward. 
From the velocity curve the value of the gradient a is 
(4,920— 4,870) /50 = 1 ft/sec/ft of depth. It follows 
that the radius is 4,900 ft. The curvature of the ray in 
this layer is therefore much greater than in the iso- 
thermal layer. 

2.2.3 Rays in a Composite Gradient 


that the centers of the circular rays usually fall be- 
yond the limits of the drawing board. Moreover, 
it is desirable to use a large vertical scale and a 
small horizontal scale for such diagrams. This dis- 
tortion converts the circles into ellipses. Methods 
for coping with these complications have been 
devised. 4,5 

It is also possible to construct a mechanical device 
which, once it has been set up for a given velocity 
distribution, will plot many rays in a relatively short 
time. 6 

2.3 TYPICAL RAY DIAGRAMS 

2.3.i Marked Downward Refraction 

A ray diagram for typical conditions of sharp down- 
ward refraction is shown in Figure 10. It should 
always be borne in mind that the curvature of the 
rays is very much exaggerated because of the neces- 


This construction can be generalized to the case of 
two layers, in each of which the velocity gradient is 
constant, as shown in Figure 9. The radius for the 
portion AB of the ray is determined as though the 
second layer were not present. The radius for the 




Figure 9. Diagram illustrating curvature of rays in a 
composite gradient. 

portion BC is determined as though the first layer 
were absent, and the center is fixed so that BC joins 
smoothly on to A B. 

Since most velocity distributions can be approxi- 
mated by a series of such layers (see Figure 4), an 
approximate ray construction can be carried out in 
this way. Practical complications arise from the fact 


VELOCITY RANGE, YD X I0 J 



Figure 10. Ray diagram with sharp downward re- 
fraction* 


sary contraction of the horizontal scale. In Figure 10 
the ratio of horizontal to vertical scale is 75. Figure 
11 shows a portion of the same diagram drawn on an 
undistorted scale. 

The contracted horizontal scale also exaggerates 
the inclination of the rays with the horizontal. This 
is shown in Figure 12, the numbers being the true 
angles in degrees and the lines showing the angles as 
plotted on the diagram. The part of the beam above 
the axis is considered to have positive inclination; the 
part below the axis, negative inclination. In the case 
of a directional transducer, nearly all the energy is 
concentrated in a cone of about 10 degrees opening. 
Hence a judicious selection of rays with initial incli- 
nations of between 5 and 6 degrees on either side of 
the axis will provide a sufficiently complete picture of 
the paths followed by the sound rays. 

The velocity-depth graph of Figure 10 shows 
three layers in which the velocity gradient is con- 


16 


THE REFRACTION OF SOUND 


I- 


I 

I- 

Q. 

U 

o 


RANGE, YD 



Figure 11. Diagram of part of Figure 10 drawn with undistorted scale. 


stant. The projector is at a depth of 16 ft. Three 
rays are drawn. 

1. The ray that leaves the projector at — 6 degrees, 
and which may be considered as the lower boundary 
of the main lobe of the projected beam of sound. The 



Figure 12. Diagram showing how the inclination of 
the rays is distorted in the conventional ray diagram. 


dimensions of the figure do not permit the inclusion 
of the + 6 degree (upper bounding) ray. 

2. The ray leaving the projector horizontally— the 
axial or zero degree ray. This ray is shown bent 
sharply downward. 

3. The ray leaving the projector at +1.4 degrees; 
this angle was chosen because this ray is tangent to 
the surface. These three rays are also shown on 
Figure 11 with an undistorted horizontal scale. 

The most striking feature of this ray diagram is 
that all the sound is confined to a very limited region 
and that beyond about 500 yd from the projector 
the surface casts a shadow. The explanation of this 
shadow is as follows. The outer rays of the upper half 
of the sound beam fall on the surface and are reflected 


there. A ray of a certain critical inclination is re- 
fracted downward so that its inclination when it 
reaches the surface will be zero. All rays with inclina- 
tions greater than this critical value are reflected back 
by the surface inside the region bounded by the ray 
tangent to the surface. 

A ray with less initial inclination will not reach the 
surface but will curve down inside the critical ray; 
the 0-degree ray illustrates this. The critical ray in 
the present example is the 1.4-degree ray. It bounds 
the direct sound field and for this reason is called 
the “limiting ray.” 

Except for sound scattered or diffracted from the 
direct sound field, the shadow should be a region of 
silence. This picture is approximately a true one; 
observations made under conditions of strong down- 
ward refraction show a sharp drop of from 30 to 40 
db in the sound level near the range indicated by the 
limiting ray. Experimental measurements of the 
transmission of sound under conditions like these are 
discussed in Chapter 3. 

232 Isothermal Layer and Thermocline 

Another common type of thermal distribution is 
the kind shown in Figure 4. This shows an isothermal 
layer at the surface, below which there occurs a sharp 
negative gradient. In the isothermal layer, the ve- 
locity gradient is positive because of the pressure 
effect; this is shown in Figure 4B. About 90 per cent 
of all the bathythermograph records from all over the 
world show this type of thermal structure. The sound 
velocity graph and ray diagram corresponding to this 
example are shown in Figure 13. 

The theory again predicts a shadow, limited by 
the ray which is horizontal at the level of maximum 
velocity. The rays above the limiting ray are re- 
fracted upward and are ultimately reflected at the 
surface. Those below the limiting ray enter the thermo- 
cline and are there refracted downward. The sound 
beam is split along the limiting ray into an upper and 
lower section; hence the term “split-beam pattern” 
is commonly applied to this type of ray diagram. 


SOUND INTENSITY AND RAY DIAGRAMS 


17 


VELOCITY 
4895 4900 



RANGE, YD X I0 3 
0 12 3 4 



Figure 13. Ray diagram for the case of an isothermal 
surface layer. Dotted curves represent rays reflected 
from the surface into the theoretical shadow. 


As in the previous case, one would expect the 
shadow beyond the limiting ray to be a region of 
relative silence. Actually the shadow in Figure 13 
differs from that in Figure 10 in that it is penetrated 
by surface-reflected rays such as those designated by 
A and B. Since the surface reflects approximately all 
of the incident sound energy, it is obvious that the 
shadow in Figure 13 will not be as complete as the 
one in Figure 10. Also, in the sound velocity graph, 
the corner at the point C of maximum velocity is 
actually rounded instead of being sharp as shown. 
When this rounding is properly introduced into the 
theory, the “shadow” is found to be actually a region 
into which few direct rays, rather than none at all, 
penetrate. 

Experiments show that there is no noticeable 
shadow under these conditions. The intensity at a 
given depth is found to decrease gradually with in- 
creasing range and shows no abrupt drop as the limit- 
ing ray is crossed. The decrease of intensity is more 
rapid below the split point than above. A more de- 


Figures 14 and 15. Figure 14 illustrates the case where 
two limiting rays bound the field. Figure 15 shows a 
velocity distribution resulting in what is called a 
sound channel. All rays leaving the projector between 
the two rays A and B are alternately refracted up and 
down. They are consequently confined to a certain 
layer, to which the above term is applied. The trans- 
mission loss in sound channels is exceptionally low, 
and long echo ranges are possible. 

In the open sea sound channels are rare and transi- 
tory in the upper layers, since the thermal conditions 
causing them are unstable (see Chapter 4). Near the 
mouths of large rivers, where salinity conditions cause 
changes in sound velocity, it is possible to have stable 
sound channels in the surface layers. 

At great depths, where the temperature is nearly 
constant, the pressure effect causes the sound velocity 
to increase with depth, and there is a permanent 
sound channel, as described in Section 2.1.2 and 
Figure 2. Experiments with the transmission of sound 
in the deep sound channel are discussed in Section 3.1 . 


2.4 SOUND INTENSITY AND 

RAY DIAGRAMS 

2.4.i Ray Divergence and Intensity 

The effects of refraction have thus far been pre- 
sented in a black-and-white picture of silent shadows 
and regions of direct or reflected sound. This was the 
earliest form of theory on which echo-range pre- 



Figure 14. Diagram showing sound field bounded by 
two limiting rays. 


Figure 15. Diagram illustrating the formation of a 
sound channel. 


tailed discussion of transmission under conditions 
such as these is given in Chapter 3. This decrease in 
intensity in this region is known as the layer effect and 
will be discussed further in Section 2.4. 

233 Crossing Rays and Sound Channels 

Other thermal structures result in the sound field 
conditions illustrated by the ray diagrams shown in 


dictions were based, and gave better results than 
no theory at all. However, it has since been learned 
that the shadows are not silent and that there are 
marked variations of intensity within the field of 
direct sound. 

Even before this experimental knowledge was 
obtained, attempts had been made to elaborate the 
ray theory to enable the calculation of intensity 
changes in the direct field. This intermediate theory 
is still useful for some purposes even though it also 


18 


THE REFRACTION OF SOUND 


X 

H 

cl 

UJ 

Q 


VELOCITY 


SOURCE 



h 





predicts completely silent shadows that are not 
observed. 

The general idea of this theory is to consider pyr- 
amids or cones of rays, the vertices of which are at 


the source of sound. Figure 16 A shows such a pyramid 
of straight rays. Neglecting losses caused by absorp- 
tion and scattering, all of the power radiated into this 
pyramid by the projector will remain inside the 


SOUND INTENSITY AND RAY DIAGRAMS 


19 


SOUND VELOCITY, FT/SEC 
4850 4900 


RANGE, YD 



RANGE, YD 




Figure 17. Diagram illustrating the calculation of theoretical intensities for typical ray diagram. (A) Bathythermo- 
gram, (B) ray diagram, (C) intensity contours, (D) anomaly graph for several depths. 


pyramid as it travels outward. The energy flow (power 
per unit area) is consequently inversely proportional 
to the cross section of the pyramid. As the cross 
section increases, the energy flow, or intensity will 
decrease. Since the cross section increases as the 
square of the range r, the intensity will decrease 
according to the inverse square law discussed in 
Section 1.2: 



Figure 16B shows the same pyramid as refracted 
by a constant- velocity gradient. The cross section of 
the pyramid at any range is seen to be approximately 
the same as at the same range in Figure 16 A. 
The two may be considered equal in a practical 
calculation. Consequently, in a layer of constant 
velocity gradient the intensity also follows the 
inverse square law. 

Figure 16C shows two layers with different grad- 
ients. The rays diverge abruptly as they enter the 
lower layer, increasing the cross section of the pyra- 
mid; this results in a decrease of the intensity. The 
horizontal spread w in C is the same as in A ; the 
cross-sectional areas of the two pyramids are there- 


fore in the ratio of the heights h'/h. It follows that 
the intensity I in Figure 16C is given by 



Converting this to decibels, we have 

L = S — 20 log r — 10 log ^ ^ , (4) 

and the transmission loss is 

H = 20 log r + 10 log (^j . (5) 

The second term is the transmission anomaly due to 
refraction. Hence this theory predicts that the trans- 
mission anomaly should be 

A = 10 log (6) 

2.4.2 Theoretical Intensities for Typical 
Ray Diagrams 

The calculation of the transmission anomaly A, 
using equation (6), can be carried out for various 


20 


THE REFRACTION OF SOUND 



Figure 18. Same as Figure 17 for a case of downward refraction. 


points in the sound field, once a sufficient number of 
rays have been plotted. At a given point, the value of 
h is given by 

h = rAd, (7) 

where r is the range to the point and Ad is the angular 
separation between adjacent rays as they leave the 
projector. The value of h' can be approximated with 
sufficient accuracy for practical purposes by measur- 
ing the vertical displacement between the two ad- 
jacent rays at the depth and range of the point under 
consideration, provided the value of Ad has been 
chosen sufficiently small. 

The results of such calculations can be presented 
graphically in various ways, as illustrated in Figures 
17 and 18. Figure 17A is a typical bathythermogram 
showing an isothermal layer and thermocline. The 
corresponding ray diagram is shown as B. Figure 
17C shows a series of contours on which the sound 
level is constant. They are identified by the values 
of transmission loss in db. Above the thermocline 
they represent the loss calculated from the inverse 
square law. It is seen that, above the thermocline, 
these contours are, in general, farther from the pro- 
jector than they are below the thermocline, and also, 
that they are more widely spaced above than below. 


Throughout the whole shadow (shaded area) the 
calculated intensity is zero, and the transmission loss 
is consequently infinite. ~ * 

A second method of presenting the results is shown 
by Figure 17D. The transmission anomaly was cal- 
culated for various points. Holding the depth of the 
point constant (say at 70 ft) and allowing its distance 
from the source to vary, one obtains a series of values 
that can be plotted as a curve (see curve marked 70 
ft on Figure 17D). These graphs are smooth curves 
when the depth is greater than that of the thermo- 
cline. When the point is above the thermocline, how- 
ever, the transmission anomaly is practically zero 
until the point reaches the shadow zone, when it 
suddenly becomes infinite. 

This discontinuous change in the transmission 
anomaly is partly due to the approximate velocity- 
depth curve used in the calculation (see above). If 
these approximations were eliminated from the calcu- 
lation, the change at the shadow boundary would 
not be so abrupt, and the curves would not drop so 
far. No calculations on this point have been made, 
partly because the available thermal data is not ac- 
curate enough to yield definite results. These theoreti- 
cal values of the transmission anomaly will be 
compared with the observed values in Chapter 3. 


SOUND INTENSITY AND RAY DIAGRAMS 


21 


The Layer Effect 

The very marked increase in the transmission 
anomaly in the thermocline has important operational 
implications. From Figure 17C it appears that if at a 
range of, say, 1,000 yd a hydrophone is lowered to 
a depth of 75 to 80 ft, it will enter a region where the 
sound transmission was poorer by nearly 10 db than 
it is 20 to 25 ft higher. The sudden increase of the 
transmission loss in the thermocline is called the 
layer effect . The importance of the layer effect is 
enhanced by the great prevalence of this type of 
thermal pattern in the ocean all over the world. It 
will be further discussed in Chapter 3. 

Figure 18 shows corresponding diagrams for a case 
of downward refraction. They will be compared with 
experiment in Chapter 3. 


243 Preview 

At this stage it would appear logical that we con- 
sider next the contributions of absorption and scat- 
tering to the transmission anomaly. Equally urgent, 
however, is a more intimate acquaintance with the 
nature of the ocean, the medium through which the 
sound travels. 

Because of the complexity of the subject, it was 
decided that at this point it would be more ad- 
vantageous to introduce the experimental study of 
transmission. This is therefore done in Chapter 3. 
Following this discussion, the essentials of ocean- 
ography pertaining to sound transmission are 
presented in Chapter 4. A detailed discussion 
of scattering and absorption will be found in 
Chapter 5. 


Chapter 3 

THE TRANSMISSION OF SOUND IN THE SEA 


T he various factors that contribute to produce 
the transmission anomaly, as summarized in Sec- 
tion 1.3.4, have all been investigated experimentally 
to a greater or lesser extent. The variability in the 
transmission loss was first observed in actual echo- 
ranging operations at sea. In certain areas, the ranges 
achieved in the afternoon of clear, relatively calm 
days were found to be less than those obtained in the 
mornings. Numerous explanations were advanced, 
but the true reason was discovered by the Woods 
Hole Oceanographic Institution as the result of ex- 
periments performed in cooperation with the U. S. 
Navy. The effect was found to be caused by the heat- 
ing of the upper layers of the ocean by the sun. This 
observation resulted in the theoretical investigations 
described in the preceding chapter. The conclusions 
based on this theory were in their turn subjected to 
rigorous experimental investigation, and it is with 
these experiments that the present chapter deals, 
together with the attempts to determine the role 
played by the other factors mentioned. 

Most of the experimental work was done using 
sound of supersonic frequencies, generated by stand- 
ard sonar projectors. More recently, however, the 
transmission of sounds of sonic frequencies has been 
investigated to some extent, and promises to provide 
a fruitful field for extensive research. For certain 
phases of the research program, sound produced by 
underwater explosions was found to be ideally suited, 
for reasons that will become clear in the following 
paragraphs. These three kinds of experiments will all 
be considered in this chapter, the experiments with 
explosive sound being discussed first. 

3.1 THE SOUND OF UNDERWATER 
EXPLOSIONS 

The suitability of explosive sounds for investigat- 
ing some features of sound propagation is well known 
to acoustic engineers. In making a preliminary sur- 
vey of a room that is to be acoustically treated, they 
often use a handclap as the experimental sound. The 
shortness of the duration of the original sound makes 
it readily possible to hear echoes distinctly and to 
estimate their relative intensity. In geophysical and 
underwater sound investigations, blasting caps and 


other explosives are generally employed. While the 
sound produced by a blasting cap exploding under 
water is not quite so simple as that of a handclap, it 
does have some of the characteristics of the latter, 
as well as much greater intensity. 

3.1.1 The Explosion Bubble and 
Its Oscillation 

The explosion suddenly creates a relatively small 
bubble of gas at a very high temperature and pres- 
sure. The pressure is imparted to the water and is 
radiated as a sound wave of extraordinary intensity 
— a “shock” wave, which, because of the enormous 
pressure, differs from ordinary sound waves in some 
particulars. A shock wave bears a similar relation to 
an ordinary sound wave as that of a large breaker 
on a beach to an ordinary water wave. One effect, 
due to the high pressure, is that the shock wave has 
a higher velocity than ordinary sound waves; how- 
ever, at reasonable distances, its velocity begins to 
approach the normal value. 

The gas bubble created by the explosion expands 
and sets the surrounding water in motion. The ex- 
pansion continues even after the pressure in the 
bubble has become much less than the normal hy- 



Figure 1 . Diagram of oscillogram of underwater ex- 
plosion, showing direct and surface-reflected pulses of 
consecutive “pokes.” 


drostatic pressure. This is because of the inertia of 
the water. The bubble finally ceases to expand and 
begins to contract; again the inertia of the water 


22 


THE SOUND OF UNDERWATER EXPLOSIONS 


23 


causes the equilibrium point to be passed, and the 
contraction continues until the pressure in the bubble 
has become very great. During this high-pressure 
phase, intense sound is again radiated. The mechan- 
ism is similar to the familiar water hammer when a 
faucet is turned off too suddenly. 

The alternate expansion and contraction is repeated 
a number of times, resulting in well-separated pulses 
or “pokes” of sound; these are shown diagram- 
matically in Figure 1. The time intervals between 
the pokes depend on the hydrostatic pressure at the 
place of the explosion, but obviously not on the dis- 
tance from the explosion or on the depth of the hydro- 
phone. The dependence on the hydrostatic pressure 
is shown in Figure 2. 9 


50 

2 40 
2 
O 
u 

U 30 


HYDROSTATIC PRESSURE, FT 
60 80 100 200 400 


20 


\ 











X 







N 

V 


X 


\ 

THIRD 
s. POKE 





X 

SEC< 

POI 

X 

DNC 

V 

l 

!' 

X 

•'« 

X. 









X 








X 









•\ 



















X 



Figure 2. Dependence of time interval between pokes 
on the hydrostatic pressure at the point of explosion. 


3.1.2 The Reflection of Sound at 
the Sea Surface 

The immediate result of the experiments with 
explosive sound was to emphasize the importance of 
the ocean surface in the study of sound transmission 
in the sea. This importance rests upon the fact that 
sound reflected from the surface interferes with that 
traveling directly. 

Time Delay of the Reflected Pulse 

Figure 1 shows each of the pokes to consist of two 
peaks, the first of which corresponds to a wave of 



Figure 3. Oscillograms showing variation of time 
interval between direct and reflected pulses. 


compression, the second to a wave of rarefaction. 
These peaks are easily seen in the oscillograms of 
Figure 3, each of which is the record of the first poke 
only. The oscillograms show a variable time interval 
between the positive and negative peaks; this time 
interval depends on the distance from the explosion 
to the hydrophone and on the depth of both the 
hydrophone and the explosion. 



24 


THE TRANSMISSION OF SOUND IN THE SEA 


It has been found that the separation of positive 
and negative peaks can be calculated quite accurately 
on the assumption that the positive peak represents 
sound that travels directly from the explosion to the 
hydrophone, while the negative one is the echo from 
the surface. The geometry of this calculation is shown 
by Figure 4. The direct sound travels over the dis- 
tance EH, while the surface echo travels the distance 
ER + RH = IH. Thus, both the time and direction of 
arrival of the echo is the same as if it originated at the 



Figure 4. Diagram of sound travel. The explosion 
occurs at E, d ft beneath the surface. The sound will 
travel via the hydrophone H , located h ft below the 
surface, either directly via EH, or by reflection from the 
surface, via ERH. In the latter case the travel distance 
is equal to IRH, where / is the image of E. 

mirror image I of the actual explosion. The reflected 
sound travels farther than the direct sound by the 
distance IH — EH. From Figure 4, 


(EH) 2 = r 2 +(h-d) 2 , 

= r 2 + h 2 -2hd + d 2 ; 

C TH) 2 = i* + (h + d ) 2 , 

= r 2 -{-h 2 -\- 2hd + d 2 . 

Subtracting one equation from the other, one finds 


The time delay At in the arrival of the echo is given by 


(IH - EH) 
c 

2 hd 

f 

rc 


( 3 ) 


where c is the velocity of sound. This law is compared 
with experiment in Figure 5. 9 

These considerations leave no doubt that the 
negative pulse is the echo reflected from the sur- 



2 hd/rc, ARBITRARY UNITS 


Figure 5. Comparison of theoretical and observed 
time delay between direct and surface-reflected pulses 
of explosive sound. 


face. Theoretical considerations lead to the predic- 
tion that the echo of a compression pulse from the 
air-water surface should be a rarefaction, and the os- 
cillograms show that this is actually the case. la ’ 2a>6a 


or 


(IH) 2 — (EH) 2 = Hid, 


IH— EH = 


4 hd 

(IH + EH)' 


( 1 ) 


If r is much greater than either h or d , as is often 
the case, IH + EH is very nearly equal to 2 r. Hence, 
approximately, 


IH — EH = 


2 hd 


(2) 


Interference of Direct and Surface-Reflected 
Rays — The Image Effect 

These oscillograms of Figure 3 also show the 
phenomenon of interference in a very instructive 
manner. When the explosion occurred at a depth 
of 200 ft, the direct and reflected pulses were 
well separated in time. At 40 ft, however, the 
negative (reflected) pulse arrived before the posi- 
tive (direct) pulse had ended; and when the charge 
was exploded at a 5-ft depth the two pulses ar- 
rived almost simultaneously. In this last instance, 



THE SOUND OF UNDERWATER EXPLOSIONS 


25 


the compression is almost completely canceled by 
the rarefaction. This interference between the di- 
rect and reflected sound is called the image effect. 
It will be discussed further in Section 3.3.2, at which 
time the quantitative aspects will be considered. 

3.1.3 Modification of the Image Effect 
by Refraction 

The manner in which refraction modifies the image 
effect is very conveniently investigated with ex- 
plosive sound. The case of simple downward refrac- 
tion is illustrated by Figure 6. As the shadow bound- 
ary is approached, the rays of the direct and reflected 
sound reaching a given point coincide more and more 



Figure 6. Diagram showing the modification of the 
image effect by refraction. 


closely. At points near the shadow boundary ( B in 
the diagram), the time delay of the surface echo 
approaches zero. In the absence of refraction, this 
would not occur until very great ranges are reached. 
This reduction of the time delay by downward re- 
fraction occurs at all ranges but is small at short 
ranges. The reduction in time delay has been ob- 
served in experiments with explosive sound, and the 
data used in Figure 5 have been selected to exclude 
conditions under which it is appreciable. 

Even more complicated effects are possible, as 
shown in the bottom diagram of Figure 6. In this 
case the rays cross, and there are two direct rays 
reaching some points such as C. Moreover, no re- 
flected rays reach such points. Consequently, the 



r= 1300 YD 


Figure 7. Oscillograms showing multiple path effects 
in explosions. 

received sound consists of two positive peaks and no 
negative one. This has been experimentally observed 
(see Figure 7). 

3 . 1.4 The Intensity of the Direct Sound 

The study of the direct-sound pulses has resulted 
in a verification of the intensity theory developed in 




26 


THE TRANSMISSION OF SOUND IN THE SEA 


RANGE, YD SOUND VELOCI T Y, FT/SEC 




Figure 8. Experimental data showing effect of refraction on transmission of explosive sound. (A) Bathythermogram 
and ray diagram. (B) Graph of calculated transmission anomaly and measured values. The dip in the anomaly curve 
at 600 yd is due to the spreading of the rays by refraction: note that there is a markedly greater spread between the 
1.2° ray and 1.3° ray than between the rays to the left and right. The rays incline more than 1.4° tend to converge 
slightly, with a corresponding decrease in the transmission loss. Beyond the 2.54° ray is the shadow, and here the 
transmission anomaly experiences an increase. 


Section 2.4.2. The intensity was measured by noting 
the maximum value attained by the pressure during 
the positive peak of direct sound, and this measured 
intensity was then compared with the theoretical 
intensity as calculated from the bathythermogram 
shown in Figure 8A. The bathythermogram shows 
that during the experiments there were three more 
or less distinct layers, in each of which the temper- 
ature gradient was negative and nearly constant. 
The explosion occurred near the top of the second 
layer, while the hydrophone was deep in the third 
layer. From this data, a detailed ray diagram was 
carefully constructed, rays leaving the source being 
plotted at intervals of 0.1°. It will be noted that 
the 1.0°, 1.1°, and 1.2° rays are quite close to- 
gether and have their vertices in the second layer. 


The 1.3° ray is the first of the plotted rays which 
penetrate the top layer, where the gradient is 
smaller. Consequently, there is a marked diver- 
gence of this ray from the previous three. The rays 
leaving the explosion at steeper angles all penetrate 
the first layer, and their divergence diminishes with 
increasing angle but remains greater than that of 
the rays whose vertices are in the second layer. 

These peculiarities of the ray diagram result in the 
anomaly graph shown in Figure 8B, which has a 
marked dip between 600 and 700 yd and then rises 
out to the shadow boundary at about 2,000 yd. The 
experimental points scatter considerably but confirm 
the general trend between 600 and 1,500 yd. Be- 
tween 1,500 yd and the shadow boundary at 1,900 
yd, the observed values are too low. Beyond the 



THE SOUND OF UNDERWATER EXPLOSIONS 


27 


shadow boundary, theory predicts that there should 
be no sound, but, experimentally, some was detected. 

It may be concluded that the ray theory of in- 
tensities is valid except near the shadow boundary. 
The reasons for the departures in this region are not 
simple, but one major factor is undoubtedly the 
difficulty of distinguishing the direct and surface- 
reflected pulses. Their overlapping and partial can- 
cellation can be invoked to explain the low observed 
values in the 1,500 to 1,900-yd region, but it cannot 
explain the weak sound that is observed beyond the 
shadow boundary. 

MICRO-SECONDS 


O K)0 200 300 400 500 



Figure 9. Oscillograms made at increasing distances 
from the explosions. 

3.1.5 The Sound in the Acoustic Shadow 

Figure 9 shows a series of oscillograms made at 
increasing distances from the explosions. At shorter 
ranges it is easily possible to distinguish the direct 


compressional pulse from the reflected rarefaction. 
As the shadow boundary is approached, this becomes 
more difficult and the maximum pressure diminishes 
rapidly. Moreover, there is an increase in the time 
elapsing between the first perceptible increase in 
pressure and the attainment of the maximum value. 

Both these effects become more pronounced be- 
yond the shadow boundary, and the disturbance 
tends to become oscillatory, with several maxima 
and minima. The time between successive maxima 
appears to increase with range, approaching 300 
microseconds. 

No complete explanation of these phenomena has 
been given. Since they are similar to others that will 
be described below, a discussion of proposed ex- 
planations will be given in Section 3.2.3. 

3 . 1.6 Explosions in the Permanent 
Sound Channel 

The transmission of the sound of explosions oc- 
curring at great depth has been investigated by the 
Woods Hole Oceanographic Institution. Such sounds 
have been heard at great distances : the explosion of 
X A lb of TNT was heard at a distance of more than 
800 miles, and that of a blasting cap at a distance 
of 75 miles. These remarkable results are a conse- 
qu3nce of the permanent sound channel that has been 
described in Chapter 2. 

When both the sound source and hydrophone are 
at depths near the minimum of the velocity, there 
are many rays joining them. A few of these have 
been plotted schematically in Figure 10 for the veloc- 
ity distribution shown at the right. Several different 
kinds of rays can be distinguished. Those which are 
roughly sinusoidal and do not reach either the sur- 
face or bottom are called the sound channel [*8C] 
rays. Those which are reflected at the surface but 
are refracted upward before reaching the bottom are 
called RSR rays. Those reflected at both surface and 
bottom are the R rays. The horizontal ray at the 
minimum sound velocity is called the axis of the 
channel. 

The times required to traverse the different ray 
paths will not all be equal, with the result that a 
single pressure pulse of the original wave will cause 
a large number of “arrivals” at the hydrophone. 
This is the same phenomenon as shown on Figure 7 
but, under the conditions being discussed, as many as 
100 arrivals have been distinguished (see Figure 11). 


28 


THE TRANSMISSION OF SOUND IN THE SEA 


RANGE, YD X I0 3 


VELOCITY, FT/ SEC 



mmm 


PASS BAND 
CPS 

DEAD 

16-64 

250-1000 

250-1000 

1000-4000 

64-250 

64-250 

TIME/ 

SIGNAL 



SC ft tiff 
RSR f t f M f f 
R ♦ M 

t FIRST OBSERVED SC 


Figure 11. Oscillograms of sound transmitted in the deep sound channel. The arrival times of the sound, via several 
paths, are indicated by the arrows. 


The first sound to arrive will be that which has 
deviated farthest from the axis of the channel and 
thus has spent most of its time in regions of high 
velocity. It will arrive via that ray which has crossed 
the channel axis the smallest number of times. The 


second arrival makes one more crossing, the third, 
two more. In Figure 10 the rays are numbered roughly 
in the order of arrival; sound traversing the two 
rays numbered 2 will arrive practically simultane- 
ously. 




THE TRANSMISSION OF SUPERSONIC HORIZONTAL BEAMS 


29 


These remarks apply separately to the SC, RSR, 
and R rays; in general, the SC sounds arrive first, 
then the RSR, and finally the R sounds. The first 
SC arrivals are weak and separated by long intervals ; 
subsequent arrivals increase in intensity, and the 
intervals decrease, the whole resulting in a final 
crescendo followed by an abrupt termination of the 
sound. This can be followed on Figure 11 by noting 
the arrivals indicated by the upper row of arrows. 

The RSR sounds have the same kind of time pat- 
tern, but do not show the crescendo of intensity. The 
R sounds have the reverse pattern. The early R ar- 
rivals are strong and separated by short intervals, 
and show a diminuendo of intensity and a slowing 
tempo. The earliest R’s sometimes come in before 
the SC’s but continue to arrive after the SC’s have 
terminated. 

The possibility of using this technique for long- 
range signaling has been considered, and particularly 
for the location of airmen forced down at sea. 

3.1.7 Summary 

To sum up, the study of explosive sounds shows: 

1. The signal received at a given point in the 
deep ocean will consist of sound that has been re- 
flected from the surface, in addition to that which 
travels directly from the projector to the hydrophone. 
At the surface the incident sound experiences a phase 
shift of half a cycle on reflection, or, in other words, 
a wave of compression is reflected as a rarefaction. 
The surface-reflected sound, therefore, tends to in- 
terfere with the direct sound. 

2. The measured sound intensity of the direct rays 
compares quite accurately with the intensity cal- 
culated from refraction theory, except in the region 
near the shadow boundary, and in the shadow itself. 

3. The deep sound channel to be expected below 
the permanent thermocline actually does exist and 
may be a useful channel of communication. 

3.2 THE TRANSMISSION OF SUPERSONIC 
HORIZONTAL BEAMS 

3.2.1 Description of the Experiments 

Experimental Procedure 

While experiments with explosive sound were in- 
structive and provided important contributions to 


the knowledge of the transmission of underwater 
sound in general, the behavior of sound of the fre- 
quencies and intensities currently used in echo rang- 
ing was naturally of more immediate interest. 

An extensive program of experiments was under- 
taken in 1943 by the University of California in 
cooperation with the U. S. Navy Electronics Lab- 
oratory [NEL], formerly U. S. Navy Radio and 
Sound Laboratory [USNRSL] . Two vessels were used 
in the work. One carried a standard echo-ranging 
projector which transmitted 24 kc signals. The other 
vessel was equipped with hydrophones that could 
be lowered to any depth less than about 500 ft, and 
with oscillographs; the latter provided a permanent 
record of the experiment. The distance between the 
two vessels was measured by transmitting radio 
signals simultaneously with the sound signals 
and recording the difference in their arrival times 
at the receiving ship. Knowing the velocity of 
sound, an accurate measure of this distance was 
obtained. 

The simplest experiments were performed as fol- 
lows. The receiving vessel was allowed to drift, and 
the transmitting vessel ran on a straight course, 
opening or closing the range. During the whole of 
the run, the sound beam was directed at the receiv- 
ing vessel by using pelorus bearings from the bridge, 
which were repeated in the sound room. The receiv- 
ing vessel suspended its hydrophones at depths which 
were kept fixed during the experiment. The oscillo- 
grams of the received sound were developed ashore 
and measured. The results were expressed as trans- 
mission anomaly. 

Early experiments of this sort had been performed 
by the Naval Research Laboratory [NRL] 16 but were 
difficult to interpret and did not receive the recogni- 
tion that they merited. 

Treatment of Data 

Data obtained on two typical runs are shown in 
Figures 12 and 13. In each case, two hydrophones 
were used, one at a depth of 300 ft, the other at a 
depth of 50 or 30 ft. During the period covered by 
Figure 12, the temperature gradient in the upper 
100 ft averaged about 0.03° F/ft, and the temperature 
decrease began at the surface. During the period 
covered by Figure 13, the upper 200 ft of the ocean 
was isothermal, and a very rapid decrease of several 
degrees (a thermocline) occurred just below this 
depth. The differences between the two figures show 


30 


THE TRANSMISSION OF SOUND IN THE SEA 


RANGE, YD 



Figure 12. Observed transmission anomaly of a single 
run. Negative gradient at surface curve 1 shows the 
level with a shallow hydrophone (50 ft), curve 2, those 
with a deep hydrophone (300 ft). The squares A and B 
indicate the range at which the limiting ray crossed 
the horizontal at the depth of the hydrophone. 

clearly that the temperature distribution affects the 
transmission loss. 

Too much reliance cannot be placed on the results 
of any single experiment ; the variability of the ocean 
as a medium of sound transmission is so great that 
the next experiment may give quite different values. 

Consequently, the procedure was to make a number 
of experiments under similar thermal conditions and 
to average the experimental measurements at a 
given range. These average values were then studied 
first, with a view to determining general principles. 

The next step was the study of the departures of 
single individual values. It was recognized that these 
departures from the averages were often as impor- 
tant, from a practical point of view, as the averages 
themselves. 

In this section, the emphasis will be on average 
results and general principles. The discussion of the 
departures of single experiments from the average 
will be postponed to Section 3.5. 


3.2.2 Major Factors Influencing 

Transmission from a Shallow Projector 

The general objective of the study of the trans- 
mission records was to establish the effects caused 
by the changing conditions in the sea. When these 
changes are numerous and complex, as they are in 
the upper layers of the ocean, this is difficult to do 
unless a good theory is available. As was mentioned 
at the beginning of this chapter, the early discoveries 
led to the general conclusion that the changeability 


RANGE, YD 

Q 0 1 1000 2000 3000 4000 5000 



o 

w 40 
to 


2 

to 

z 

< 

£ 601 

Figure 13. Observed transmission anomaly of a single 
run— isothermal layer 200 ft deep at the surface. Curve 
1 shows the levels with a shallow hydrophone (30 ft), 
curve 2 those with a deep hydrophone (300 ft). The 
greater anomaly in the second case indicates layer effect. 

of underwater sound transmission should be ascribed 
chiefly to the temperature distribution. 

The ray theory, discussed in Chapter 2, was used 
as a guide in the interpretation of the data. It has 
been mentioned that this theory does not account 
adequately for all the facts in the transmission of 
explosive sounds and this is true to an even greater 
degree for supersonic sound. However, some of its 
predictions have been verified in a satisfactory man- 
ner and it has served a useful purpose in the analysis 
of the data. 

In the succeeding paragraphs we shall summarize 
the major results of the experimental study of the 
transmission of sound in the sea in the form of con- 
clusions that have been definitely established. These 
conclusions will be compared qualitatively with the 
ray theory. We shall then, in Section 3.2.3, proceed 
to a more detailed, quantitative comparison of ray 
theory and experiment. 

The Dependence of Transmission on D 2 

Conclusion 1. The transmission of supersonic sound 
is very strongly dependent on the depth at which the first 
appreciable decrease of temperature occurs. 

With present bathythermographs, the smallest 
temperature difference that can be established with 
certainty is about 0.3° F. Hence this depth will be D 2 , 
according to the bathythermogram code system de- 
scribed in Section 2.1.5. 

General Features of the Anomaly Curves. Conclusion 
1 is established by the data shown in Figure 14. All 
these data were obtained with the hydrophone at 
about the same depth as the projector, about 16 ft 



THE TRANSMISSION OF SUPERSONIC HORIZONTAL BEAMS 


31 


§ RANGE, YD 



Figure 14. Average transmission anomaly under var- 
ious oceanographic conditions: Curve 1 — 0 ft < Z) 2 

< 5 ft; Curve 2 — 5 ft < D 2 < 20 ft; Curve 3 — 20 ft 

< D 2 < 40 ft; Curve 4 — 40 ft < D 2 < 80 ft; Curve 

5—80 ft < D 2 < 300 ft. 

below the surface. This fact is important, for reasons 
that will become clear presently. 

The experiments were classified into five groups 
according to the values of D 2 . For each group the 
values of the transmission anomaly at given ranges 
were averaged, yielding the five curves of Figure 14. 

These curves show very clearly the progressive 
increase in the transmission anomaly as D 2 increases. 
Considering the curves individually, it is seen that 
in all cases the transmission anomaly increases with 
range. The significance of the differences between 
the curves will be more easily comprehended 
if the reader will refer to Figures 10, 17, and 18, 
Chapter 2. 

Isothermal Layer Present. Curves 4 and 5 of Figure 
14 show the transmission anomaly when D 2 is greater 
than 40 ft. The corresponding typical ray diagrams 
for these conditions are represented by the ones in 
Figure 17, Chapter 2. A hydrophone at 16 ft depth 
would be in the theoretical direct sound field out 
to quite long ranges. Under these conditions the 
anomaly graph is practically a straight line, and 
this linear relation continues to be valid from 10,000 
to 15, 000 yd. 

In a general way, this linear increase of the anom- 
aly with range is observed in the graphs of individual 
measurements, such as curve 1 on Figure 13, as well 
as of averaged ones; but the graphs of individual 
measurements often show maxima and minima that 
are as yet unexplained. 

Negative Surface Gradients Present. When D 2 is 
less than 20 ft, the transmission-anomaly graphs are 
curved and drop rapidly to a value of about 40 db 
for the anomaly; this is shown by curves 1 and 2 on 


Figure 14. This condition is illustrated by the bathy- 
thermograms and the ray diagrams in Figures 10 
and 18, Chapter 2. It is seen that a hydrophone 
at 16 ft depth would be in the shadow at very 
short ranges. 

The anomaly curves show a tendency to become 
horizontal at longer ranges. While it is difficult to 
measure such large values of the transmission anom- 
aly at long ranges, because of the interference from 
various sources of noise, there is reason to believe 
that this tendency is real. 

This description of the average curves again applies 
in a qualitative way to the curves of individual 
experiments, such as curve 1 on Figure 12. 

Dependence of Transmission on Depth of 
Hydrophone 

The second conclusion based on experiment is the 
following: 

Conclusion 2. The transmission of supersonic sound 
from a directional projector mounted on a surface ves- 
sel is very strongly dependent on the depth of the 
hydrophone receiving the sound. 

This conclusion is established by the data of 
Figures 15 and 16, which show curves of average 
transmission anomaly measured with hydrophones 
at different depths. Thermal patterns were of various 
kinds, but D 2 in all cases was less than 30 ft. In these 
figures, curve 1 applies to the shallow hydrophone, 
curve 2 to the deeper one. In both figures it is seen 
that lowering the hydrophone improves the trans- 
mission, because curve 2 lies above curve 1 in each 
case. Reference to Figure 10 or 18 of Chapter 2 will 
show that this is in general agreement with the ray 
theory. When D 2 is small, the negative gradient near 
the surface will be large, and the sound rays are bent 
down in a marked manner. At medium or short 
ranges the sound beam may be expected to pass 
below a shallow hydrophone, whereas a deep hydro- 
phone will be in the beam. 

An exception to this may occur at very short 
ranges, however; the sound beam may pass above 
the deeper hydrophone while it strikes the shallower 
one, the beam not having yet been bent downward 
appreciably at these short ranges. That this occurs 
is borne out by the data of Figure 16, where curve 2 
is seen to cross below curve 1 at about a 400 yd 
range ; that is to say, at this range the transmission 
to the shallower hydrophone is better. 


32 


THE TRANSMISSION OF SOUND IN THE SEA 


RANGE, YD 



Figure 15. Average transmission anomaly — depend- 
ence on hydrophone depth Z) 2 < 5 ft. Curve 1 — 
depth of hydrophone < 25 ft; Curve 2 — Depth of 
hydrophone 50 to 100 ft. 

Dependence of Transmission on the Depth at 
Which a Thermocline Occurs 

The relation of transmission to hydrophone depth 
is completely reversed when D 2 is greater than 40 ft. 
Under these conditions there is usually a more or 
less marked thermocline just below the depth D 2 . 
The following conclusion has been found to apply 
to this case. 

Conclusion 3. If there is a sharp thermocline , the 
depth at which it occurs influences the transmission. 

The experimental data are shown in Figure 17. 
Conclusion 3 is closely related to conclusion 2, and 
Figure 17 is a confirmation of both conclusions 2 
and 3. The anomaly curve for the deeper hydrophone 
is in this case below that for the shallower one. 

Figure 17 of Chapter 2 is a typical illustration of 
the case when D 2 is greater than 40 ft. It appears 
from a study of this ray diagram that the experi- 
mental data again provide a qualitative confirmation 
of the theory based on ray acoustics. The beam 
splits at the depth where the sound has the maximum 
velocity, and, while the shadow zone predicted by 
the theory is not observed, there is a greater loss in 
transmission below this depth, as shown by Figure 
17. This experimentally observed layer effect is 
important even though it is not so great as that 
predicted in Section 2.4. 

3.2.3 Comparison of Ray Theory and 
Experiment — Strong Negative Gradients 

The experimental results of transmission exper- 
iments will now be compared in more detail with 
those predicted by ray theory. 


RANGE, YD 



Figure 16. Average transmission anomaly — depend- 
ence on hydrophone depth, 5 ft < D 2 < 30 ft. Curve 
1 — depth of hydrophone ^ 100 ft; Curve 2 — depth of 
hydrophone $> 200 ft. 

The Limiting Range 

The transmission anomaly curves predicted by 
ray theory were shown in Figure 18 of Chapter 2. 
They show relatively small values out to the range 
of the shadow boundary, but at that range the curve 
drops suddenly to infinity. The range to the shadow 
boundary is called the limiting range , rn m . 


RANGE, YD 



Figure 17. Average transmission anomaly — depend- 
ence on depth of hydrophone D 2 $> 40 ft. Curve 1 — 
hydrophone above thermocline; Curve 2 — hydrophone 
below thermocline. 

The observed transmission anomaly curves such 
as those shown in Figure 12, while they are quite 
different in shape, also show relatively small values of 
the anomaly at short ranges, followed by a rapid but 
continuous drop to about 40 or 50 db. Investigation 
led to the following important fourth conclusion: 

Conclusion 4- When negative temperature gradients 
exist , the rapid drop in the observed curves occurs at 
about the predicted limiting range. 

This conclusion was first established by marking 
the predicted limiting range on a large number of 
experimental curves and noting that it always falls 
on the steeply sloping part of the curve. Figure 12 




THE TRANSMISSION OF SUPERSONIC HORIZONTAL BEAMS 


33 


illustrates this procedure; the limiting ranges are 
indicated by the squares marked A and B. 

It will be recalled that experiments with explosives 
(Section 3.1.5) exhibited a similar effect, a rapid 
diminution of the maximum pressure near the 
shadow boundary. 

The Predicted Limiting Range and r4o 

A more objective method than the one mentioned 
above was then sought. This was accomplished by 
defining a range that could be determined exper- 
imentally and compared directly with the limiting 
range. Several definitions were tried with more or 
less success. The method finally adopted (more or 
less arbitrarily) was to find the range at which the 
received sound level was 40 db less than that re- 
ceived at 100 yd. This range is called r 40 and has 
been found to be a very useful empirical concept. 
It is very approximately equal to the range at which 
the transmission loss is 80 db. This follows, since 
the transmission loss at 100 yd can be calculated 
fairly accurately from the inverse square law: 
H = 20 log r = 20 log 100 = 40 db. Hence the level at 
100 yd is 40 db below that at 1 yd, and the level at 
is 40 + 40 = 80 db below that at 1 yd. 

The experimental results expressed in terms of 7*40 
are compared with ray theory in Figure 18, in which 

PREDICTED LIMITING RANGE, YD 



Figure 18. Comparison between r 40 and predicted 
limiting range. 


the values of r w are plotted against the predicted 
limiting range. If theory and experiment agreed 
absolutely, the points representing r4o would all lie 
on the 45-degree line through the origin, shown in 
the figure. While the points scatter considerably, 
there is evidence of a tendency for them to cluster 


about the 45-degree fine, sufficient to justify the 
conclusion that this is not accidental. The ray 
theory is thus not verified in detail, but does give a 
qualitative account of the facts. 

The Inadequacy of the Ray Theory 

There has been much speculation about the 
reasons for the differences between the ray theory 
and experiment, and some efforts have been made 
to construct a more adequate theory. A brief sum- 
mary of these efforts will be instructive. 

Effect of Diffraction. The failure to observe the 
sharply bounded, silent shadow predicted by the 
ray theory has been discussed by Pekeris. 10 ’ 11 It is 
well known that, even in the case of fight, shadow 
boundaries are not sharp. Light is diffracted around 
the edges of obstacles and does not travel along 
rays. As explained in all textbooks on physics, these 
diffraction effects increase with the wavelength of 
the disturbance, so that the ra}~ theory becomes 
less and less correct as the wavelength increases. The 
wavelength of 24-kc sound in sea water is several 
inches and much longer than the wavelength of 
fight, so that considerable diffraction of sound may 
be expected. Pekeris has made calculations which 
show that the predicted effect due to diffraction is 
large enough to explain why the transmission anom- 
aly curve has a gradual slope as it crosses the limiting 
range, instead of dropping to infinity, as seen in Fig- 
ure 18 of Chapter 2. However, the quantitative agree- 
ment between this diffraction theory and the meas- 
urements is not exact. Further experiments designed 
specially to check the theory would be of interest. 

Effect of Scattering. Another possible explanation 
of the sound observed in the shadow is the scatter- 
ing by obstacles suspended in the sea. The scattering 
of fight by dust particles, snowflakes, etc., in the 
atmosphere is a familiar phenomenon and is known 
to be responsible for the many changes in the color 
of the sky and in the visibility of objects. The scat- 
tering of sound corresponding to this is known to 
occur in the sea. It is probable that this is the 
explanation for the upward curvature, at longer 
ranges, of curves 1 and 2 on Figure 14. No final 
conclusion on this topic has been reached, but 
some interesting calculations are presented in 
Chapter 5. 

The Effect of Thermal Microstructure in the Sea. A 
final reason for departures from the calculations is 
found in their approximate nature. In making them, 


34 


THE TRANSMISSION OF SOUND IN THE SEA 


it is assumed that the temperature at a given depth 
is the same at all points of the ocean, in other words, 
that the horizontal temperature gradient is zero. It 
is true that the horizontal gradient is very much 
smaller than the vertical gradient but it is not zero. 
The study of this thermal microstructure and its 
effect on the transmission of sound has not yet 
yielded any conclusion (Chapter 2). 


3.2.4 Comparison of Ray Theory and 
Experiment — Weak Gradients 

The inadequacy of the ray theory to explain sound 
transmission becomes still more pronounced when 
thermal conditions in the ocean are characterized by 
weak gradients or an isothermal layer near the 
surface, below which a more or less well-defined 
thermocline exists. As these conditions are the ones 
most commonly encountered over the greatest part 
of the ocean and much of the time in all regions (see 
Chapter 4), it is of special importance to study in 
greater detail the sound conditions associated with 
these thermal patterns. 

The anomaly curves predicted for this case by ray 
theory are shown in Figure 17 of Chapter 2. If the 
hydrophone depth is nearly the same as the projector 
depth, with the latter located in the mixed layer, the 
theoretical transmission anomaly is zero out to the 
limiting range and then suddenly increases to in- 
finity. If the hydrophone is at greater depths, the ray 
theory predicts a rapid increase in the transmission 
anomaly beginning at very short ranges. 

The experimental anomaly curves 4 and 5 of 
Figure 14 and those in Figure 17 (Section 3.2.2) show 
that the actual behavior of sound is entirely different. 
These curves are approximately straight lines passing 
through the origin, and the anomaly increases with 
range. (The departures from the straight line at 
short ranges are caused by the beam pattern, and 
will be ignored in the following discussion.) 

The linear relationship between the transmission 
anomaly A and the range r is an important one, for it 
leads to the introduction of the concept of the at- 
tenuation coefficient. 

The Attenuation Coefficient 


where a is an empirical number. It is the attenuation 
coefficient just mentioned; the equation (4) shows 
that it denotes the rate at which the transmission 
anomaly increases with the range. It is, therefore, 
measured in decibels per yard. 

The information concerning the attenuation co- 
efficient that has been obtained from a systematic 
study of available transmission records is summed up 
in the following paragraphs. 12 

The Dependence of a on the Depth of the Layer 

The depth to the bottom of the mixed layer varies 
from day to day and from place to place. It has been 
found that, on the average, the value of a is deter- 
mined by this depth, which we shall denote by d. On 
any one occasion, however, there are departures 
from this law. Both these facts are illustrated by 
Figures 19 and 20, in which a (in units of 10 -3 db/yd) 
is plotted against 1/d. The dots represent values of a 
obtained from single experiments. The squares are 
the averages of all measurements for which 1/d had 
a value within 0.025 ft -1 of the plotted abscissas. 
The general increase of the attenuation coefficient 
as 1/d increases, that is, as the layer becomes shal- 
lower, is apparent. 

A similar result would have been obtained if d had 
been replaced by Z) 2 , defined above. The two quanti- 
ties d and D 2 are roughly proportional. 

The Dependence of a on the Depth of the 
Hydrophone 

Another factor affecting the value of a is the layer 
effect, which has been defined and explained before. 
The source was at 16-ft depth in the mixed layer 
above the thermocline in each of the experiments. 
The hydrophone was at various depths. Those ex- 
periments in which it was above the thermocline are 
included in Figure 19, while Figure 20 is based on 
those in which it was below the thermocline. 

Comparison of the two graphs shows some evi- 
dence for the existence of a layer effect under condi- 
tions of weak surface gradients. The equations of the 
straight lines, obtained by a least squares solution to 
fit the squares, are, for the hydrophone above the 
thermocline, 


The anomaly curves have equations of the form 
A — ar (4) 


/ 170\ 

a = 10- 3 ( 2.5 + — J db/yd, 


THE TRANSMISSION OF SUPERSONIC HORIZONTAL BEAMS 


35 


I/d, FT- 


0.0 0.01 0.02 0.03 0.04 0.05 



Figure 19. Attenuation coefficient — dependence on the depth d of the isothermal layer. 


I/d, FT'' 



Figure 20. Attenuation coefficient — dependence on the depth d of the isothermal layer. 


and for the hydrophone below the thermocline, 

a = 10 -3 (4.5 H — J db/yd. 

The depth d is in feet. 

The scatter of the dots makes it obvious that these 
equations give the correct value of the attenuation 


coefficient only on the average, and that they will 
probably be in error on any one occasion. The prob- 
able error on a single occasion is about 2 X 10~ 3 
db/yd. This large error is not caused by faulty ex- 
perimentation but by unexplained changes in the 
acoustic state of the sea. This topic will be discussed 
in greater detail in Section 3.4. 


36 


THE TRANSMISSION OF SOUND IN THE SEA 



Figure 21. Successive refraction and reflection of a sound ray in shallow water with negative surface gradients. Lower 
figure shows observed transmission anomaly corresponding to this condition. M is the horizontal distance between 
successive arches of the ray. This figure illustrates the oscillograms of Figure 23. 


3 2.5 Reflection from the Bottom 

The transmission-anomaly curves discussed so far 
have been plotted from data in which the sound re- 
ceived at the hydrophone arrived either directly 
from the projector or by reflection from the surface. 
These curves will be different if the receiver records 
sound that has been reflected by the ocean bottom. 

When the sound beam is refracted downward it 
will eventually strike the bottom of the ocean, where 
some of its energy will be absorbed or scattered and 
the remainder will be reflected. The reflected beam 
(the echo from the bottom) will rise toward the 
surface but will be refracted downward once more. 
Figure 21 shows a ray leaving the projector in a 
horizontal direction and being successively refracted 
and reflected in a series of arches, or bounces. 

In deep water the bottom echoes can be ignored 
when short pulses are transmitted, since the time 
delay between the reception of the direct sound and 
the bottom echo is then so great that the two pulses 
are well separated and neither interferes with the 
measurement of the other. If long pulses are used, 
the direct signal pulse and the bottom echo pulse 


may overlap in time. During the period when both 
pulses are being received, they will interfere, and 
the resultant amplitude may be either greater or less 
during the periods when only one is coming in. 

In shallow water this interference will occur with 
short pings also, for in this case the difference in the 
arrival times of direct signal and bottom echo may 
easily be less than the duration of the signal pulse. 

Interference of Direct Signal and Bottom Echo 

The phenomenon of interference is of considerable 
importance in underwater sound transmission. It 
has already been introduced in connection with ex- 
plosive sound (Section 3.1) and will be encountered 
in other places (Section 3.3). Hence a digression on 
its theory appears warranted at this place. 

For simplicity, suppose the amplitude of the sig- 
nals received by direct transmission and by bottom 
reflection are both equal to V. These received signals 
will be alternating voltages, and, because of the 
difference in travel time of the two signals in the 
water, the two voltages will not be in phase. Let the 
phase difference be <f>; then the two signals can be 


THE TRANSMISSION OF SUPERSONIC HORIZONTAL BEAMS 


37 



A B 

Figure 22. Diagram showing the resultant amplitude 
of the direct pulse and bottom echo for variable phase 
difference 0. 

represented graphically by vectors, as in Figure 22A 
and B, or analytically by 

Direct = V cos 2t ft 

Echo = V cos (2tt ft +(/>). (5) 

During the period when both are being received, the 
resultant voltage will be the vector sum of the two, 
as shown in Figure 22. 

Considering the phase angle of the direct signal 
to be zero degrees for simplicity and applying the 
cosine law of trigonometry to the triangles of this 
figure, one obtains the following equation: 

(Resultant) 2 = V 2 + 2V 2 cos 4> + V 2 , 

= 2V 2 (1 -f-cos <£), 

= 4F 2 cos 2 (!</>), (6) 

whence the resultant amplitude is 2 V cos (J</>). 

If <f> = 0°, this amplitude will be 2V ; if <f> = 180°, 
the amplitude will be zero; for intermediate values 
of 4>, the amplitude will vary between zero and 2V. 

These interference effects are shown very clearly 
in the oscillograms of Figure 23, which are the records 
of successive pings received at various ranges. The 
first pulse of the 2,600 yd sequence shows the case 
when the direct signal and the bottom echo arrive 
at the hydrophone in phase, <£ = 0°. This type of 
pulse has been called the “transformer” type. The 
third pulse of this sequence is an example of the 
direct signal and bottom echo arriving out of phase — 
the amplitude diminishes, and a “spool” type of pulse 
results. If the phase difference were precisely 180°, 
there would be an extreme spool pulse. For inter- 
mediate values of <f>, there will be a graded series 
of pulse shapes; various types can be observed on 
the oscillograms, some of which are more compli- 
cated than can be explained by the simple theory 
outlined above. 

Successive Bottom Reflections 

The effect of the bottom on transmission measure- 
ments can be followed on Figure 23 or even more 
closely on the anomaly graph that forms the lower 


part of Figure 21, and which is based on the former. 
At ranges less than 600 yd, only the intensity of the 
directly transmitted sound was measured; compar- 
ison with the top diagram of Figure 21 shows that 
this is about the range where the beam strikes the 
bottom. From 600 to 1,200 yd, both the direct sound 
and the bottom echo could be measured separately. 
The intensity of the direct sound diminished in a 
manner that could have been predicted from the 
bathythermogram and the principles outlined 
above. 

The part of the anomaly curve that pertains to 
bottom-echo intensity rises out to about 2,000 yd; 
the upper diagram shows that the reflected beam 
approaches most closely to the surface at about this 
range. Beyond this, the curve drops again out to 
3,000 yd; at about this range a second echo, which 
has been reflected twice from the bottom, becomes 
measurable. Its rise, decline, and ultimate replace- 
ment by a third and a fourth echo are clearly shown 
on the graph. This succession of events can be fol- 
lowed quite easily on the complete oscillographic 
record of the experiment. The small sections of this 
record which are reproduced as Figure 23 necessarily 
lack the continuity which is the essential element 
in establishing the interpretation. 

Effect of Bottom Topography 

The effect of bottom topography is illustrated 
schematically in Figure 24 for a sloping bottom. 
Some measurements have been made that confirm 
this figure in a general way, but none has been made 
in as great detail as those on which Figure 21 is 
based. The ray diagram again shows the successive 
refraction and reflection of the ray which leaves 
the projector horizontally. Because of the slope of 
the bottom, it will be reflected at less of an angle 
with the horizontal than its angle of incidence; con- 
sequently, it will be bent downward before reaching 
the level of the projector. This is repeated at each 
reflection, with the result that the tops of the suc- 
cessive arches are at increasing depths. If the hy- 
drophone is near the surface, the main part of the 
reflected sound beam will not reach it. Consequently, 
even though some bottom echoes may be detected, 
their intensity will be very much less than if the 
bottom had been horizontal. 

A sloping bottom may therefore increase the in- 
tensity of sound received at a given range by a 
shallow hydrophone, but the increase will be less 
than that due to a flat bottom. 


38 


THE TRANSMISSION OF SOUND IN THE SEA 


RADIO DIRECT FIRST BOTTOM' 

SIGNAL SOUND SIGNAL REFLECTION 

□_ . __ .. 

’ — i*- 


- - — JO- 



RANGE = 

1220 YD 

RADIO 

SIGNAL 

1 

FIRST BOTTOM SECOND BOTTOM 
REFLECTION REFLECTION 


_ IL 

~*v 



S— man _ 


^ m * — ex 


RANGE- 2600 YD 


RADIO 

SI GNA L 

— J j^.. 


SECOND BOTTOM THIRD BOTTOM 
REFLECTION REFLECTION 


4> 






rtmtfmt'im'Mn'm** wwavw.V/wVvw^^ .v.v //«V^/.v.-.v>.w-,vw-«^V.w 1 . w .v V/avVwwVwvV^^^ 

RANGE=4500 YD 


RADIO 

SIGNAL 

THIRD BOTTOM 
REFLECTION 

FOURTH 

BOTTOM 

REFLECTION 

• r 

— 1 

r 

— — » <— — . . . ... 1 

r¥ 

vw.V^V^WfwWwVwM l /w.'ww l fl^VwA>,'.vyw'AVwVwiyVAv^>w/>wVw/V.vA’V.v,v', 

V..V <WW AVV/. -MW AW/. »v-w AW/ AV.V AWft/AW ^WA'vWWiVAW^WAVAV/WAWVVAVVAVA>MMVvMtW/AtVwwVAVA'/AW'AW/VWA 


-«o 


V’iYW'^VV.V^W.W>A'^V>ViV-WA',VA<A''AVA‘,VAW.’/.VA‘V//A'V>V)V,'A , /lW>AV’.' 


RANGE=6300 YD 


Figure 23. Oscillograms showing successive bottom reflection in shallow (80 fathom) water. The lower half of each 
strip follows the upper half immediately. 


THE TRANSMISSION OF SUPERSONIC HORIZONTAL BEAMS 


39 


RANGE, YD TEMPERATURE, F 

0 1000 2000 3000 4000 5000 6000 7000 30 40 50 60 70 



Figure 24. Schematic figure of successive bottom reflections over sloping bottom with negative temperature gradients. 


The Influence of Ocean Depth on Transmission 

From this discussion, certain general conclusions 
can be drawn concerning the influence of water depth 
on transmission over a flat bottom. It has been tacitly 
assumed that the projector is directional and emits 
a well-defined horizontal beam of sound. These con- 
clusions will need modification below, when trans- 
mission from nondirectional sources is considered. 
Even in the case of directional beams, these theoret- 
ical conclusions are oversimplified and must be ap- 
plied with caution to actual conditions. The ex- 
perimental results that are presented in the next 
section will indicate the nature of the complications 
to be expected. 

The fundamental parameter is M , the distance 
between successive arches in the ray diagram of 
Figure 21. This distance will increase with increasing 
water depth and decrease with increasing down- 
ward refraction. When there is only slight downward 
refraction or upward refraction, M will be very large 
or even undefined; the conclusions are completely 
inapplicable to such cases. A mathematical formula 
for M can be derived, and appears to be very useful 
in correlating the data on transmission in shallow 


water. This work is still in progress as this is being 
written. 

With some reservations, therefore, the following 
conclusions can be accepted. 

1. When the range of the hydrophone from the 
projector is less than about Y M, the transmission 
is the same as in very deep water. 

2. When the range is greater than about Yi 
the transmission will be as good or better 

than that in deep water. The amount of the im- 
provement will depend on the strength of the 
bottom echo, i.e., on the reflection coefficient of the 
bottom. 

3. As the range increases, a large number of bot- 
tom reflections is needed to bring the sound to the 
hydrophone, and the transmission loss increases. 
Theoretically, the transmission anomaly should be 
roughly proportional to the number of reflections, 
i.e., to the ratio r/M, where r is the range. This is 
indicated in Figure 21 by the straight line; there will 
be periodic departures from this law, as can be seen 
in the figure. 

4. With extreme temperature gradients in water 
of moderate depths, these maxima and minima may 


40 


THE TRANSMISSION OF SOUND IN THE SEA 



TODOS SANTOS 
PATCH: SM-3 
19 JUNE, 1945 
RUN 4D 


RANGE- KYD 


0 12 3 



Figure 25. Transmission of 24-kc sound over sand- 
mud with strong downward refraction, showing direct 
and bottom-reflected sound. 


4. Thermal gradients: 

a. In the surface layers. 

b. In the deep layers. 

5. State of the sea surface. 

The first two of these have already been sufficiently 
treated in the previous section; the others will now 
be discussed. 

Dependence on Bottom Character and 
Surface Gradients 

The range r 40 , defined above in Section 3.2.3, is a 
convenient parameter to use in the discussion. A 
large value of r 4 o means good transmission and a 
small value poor transmission. Figure 26 summarizes 
the dependence of r 40 on the factors listed above as 

d 2 ,ft 


5 10 20 40 80 160 



become very pronounced. This can be seen from 
Figure 25. 


Figure 26. Dependence of r 40 on bottom character and 
the thermal gradients in the surface layers. The latter 
are indicated by the magnitute of D 2 . The curve for 
the deep water is included for comparison. 


3.2.6 Transmission in Shallow Water 

Factors Affecting the Transmission 

The transmission of sound in shallow water is 
affected by many more factors than in deep water. 
This makes the experimental study much more dif- 
ficult, since it is often uncertain whether a given 
change is caused by one or another of the factors. 
The results discussed in this section are therefore 
more complicated and less certain than those pre- 
sented for deep water. 

The various factors affecting shallow-water trans- 
mission include 

1. The flatness of the bottom (topography). 

2. The depth of the water. 

3. The kind of material forming the bottom (bot- 
tom character). 


3 and 4a, the variable D 2 being the depth at which 
the temperature is 0.3°F less than at the surface 
(see Section 3.2.2). For comparison, a graph for deep 
water has been included. 

In constructing these graphs from the experimental 
data, some attempt has been made to allow for the 
influence of the other factors, such as the state of 
the sea surface and the thermal gradients at greater 
depths. It cannot be hoped that this attempt has 
been completely successful, but it is believed that 
the plotted values of r 40 are usually within 500 yd 
of their proper relative positions. The absolute values 
may be in error by even greater amounts, but the 
shapes of the curves are probably reasonably accurate. 

It is seen that transmission over sand bottoms is 
very good, indicating that sand reflects a large 
fraction of the incident sound. The value of r® is 
practical^ independent of the gradient in the sur- 



THE TRANSMISSION OF SUPERSONIC HORIZONTAL BEAMS 


41 


face layers, which may be rather surprising in view 
of the conclusions at the end of the previous section 
Several reasons, however, can be advanced for this 
fact. The spacing of the ray arches will be more 
strongly determined by the gradients in the deeper 
layers than by those in the upper layers. Moreover, 
the previous discussion was based largely on the 
ray that leaves the projector horizontally; the pro- 
jector used in these experiments has a beam whose 
half width is about 6 degrees. Consequently other 
rays must be considered, including some that are 
reflected by the sea surface as well as by the bottom. 
It is possible that an adequate explanation of the 
observations could be worked out along these lines. 

Rock bottoms behave very much like sand bottoms, 
but the transmission is not so good as over sand. 
Sand and mud is shown to be very similar to rock. 
It is interesting to note the sudden increase in r 4 o 
when D 2 is greater than 80 ft. While this point is 
based on very meager data, it is in accord with the 
conclusion that the transmission in shallow water 
should never be wc than that in deep water. The 
two points on the rock and on the sand and mud 
curves which apparently do not conform to this 
principle may be affected by the experimental errors 
discussed above. 

The curve for shallow water with a mud bottom 
coincides, within experimental error, with that for 
deep water. It will be concluded from this that mud 
does not reflect an appreciable amount of sound. 

Effect of Deep Gradients 

The evidence for a strong dependence of transmis- 
sion on the temperature gradient in deeper layers is 
good, although somewhat unsystematic; it is given 
in Figure 27. As a measure of the deep gradient, the 
temperature difference A between the surface and 
150 ft was chosen; in the event water depth was less 
than 150 ft, the temperature difference between 
surface and bottom was used instead. Each pair of 
graphs refers to a single bottom character, and the 
two graphs show the average anomaly as a function 
of range for small and large values of A. The averages 
extend over data for various values of the sea and 
wind force, but some residual effects of these varia- 
bles may be present. However, the differences shown 
are undoubtedly real and caused by the deep tem- 
perature gradients. They are in qualitative agreement 
with the conclusions of the previous section. The 
maxima associated with successive bottom reflections 


RANGE, YD 



Figure 27. Dependence of transmission anomaly on 
bottom character and A, the temperature difference 
between the surface and a depth of 150 ft. If the water 
depth is less than 150 ft, A denotes the temperature 
difference between the surface and the bottom. 

appeared on some (though not all) of the individual 
curves, but have been lost in the process of averag- 
ing. The large anomaly at short ranges is due to the 
great depth of the hydrophone used in these experi- 
ments; this may also be responsible for the lack of 
prominence of the reflection maxima. 

As indicated above, there is some evidence that 
transmission in shallow water is worse when the sea 
surface is rough than when it is smooth. This effect, 
however, is not so great as was once supposed. 14,15 
It so happened that most of the data for smooth 
surfaces were taken when A had small values, and 
most of that for rough surfaces when A had large 
values. Thus much of the observed effect was ac- 
tually caused by the variation in A and was erro- 
neously ascribed to changes in the sea surface. This 
incident is recorded as an illustration of the errors of 
interpretation that can occur during the study of a 


42 


THE TRANSMISSION OF SOUND IN THE SEA 


complex set of causes. However, experiments have 
now been performed on days when the wind force 
changed, with corresponding change in the sea 
surface, but no change occurred in A. They show that 
there is a definite effect of the kind described, whose 
magnitude appears to be different for various bottom 
types. 

Work in progress as this is written appears to be 
systematizing the results on transmission in shallow 
water and promises to yield a satisfactory account of 
the major phenomena. 

3.2.7 Transmission of 60-kc Sound in 
the Sea 

While most of the experimental work on the trans- 
mission of supersonic sound from one ship to another 
has been done with 24-kc sound, a fairly adequate 
amount of work has also been done at 60 kc. 

Figure 28 shows the results of an experiment in 
which pulses of 24- and 60-kc sound were emitted 
simultaneously from the same projector. This pro- 


By these means it was possible to measure the trans- 
mission anomaly for 24- and 60-kc sound under 
identical thermal conditions. At the beginning of the 
experiment shown by Figure 28, there was a constant 
negative gradient of about 0.015°F/ft in the upper 
50 ft of the ocean. From 50 to 55 ft there was a 
marked thermocline, in which the gradient was 
1.0°F/ft, and beneath this the temperature de- 
creased more slowly. It is possible that these con- 
ditions changed, both with time during the experiment, 
and also from point to point over the path traveled 
by the sound beam. 

Results shown by Figure 28 and similar graphs 
leave no doubt that the transmission of 24-kc sound 
is better than that of 60-kc sound. The difference is 
greatest when there is no marked downward re- 
fraction. 

The average of a large number of transmission 
experiments with 60-kc sound and a shallow hydro- 
phone is shown on Figure 29. This figure is directly 
comparable with Figure 14, the five curves of the 
latter corresponding to the five sets of plotted points 
on the former. Only two curves have been drawn 


RANGE, YD 



Figure 28. Simultaneous transmission of 24-kc and 
60-kc signals. Single experiment. Slight negative sur- 
face gradient, marked thermocline at 50 ft (gradient 
1 F per foot for 5 ft). Hydrophone depth 16 ft. 

jector was designed so that the 60-kc beam was of 
about the same width as the 24-kc beam used in the 
work described in the previous section ; it was much 
narrower than the 24-kc beam associated with it be- 
cause of dependence of the beam pattern on fre- 
quency. 

The two signals were received by a single hydro- 
phone but recorded separately, after being separated 
with filters. As a check, the 24-kc signals were also 
received by a second hydrophone. Both the hydro- 
phones and the projector were at a depth of 16 ft. 



Figure 29. Average transmission of 60-kc sound for 
various oceanographic conditions. Shallow hydrophone. 
Numbering of curves corresponds to that of Figure 14. 
□ 0 ft < D 2 < 5 ft 
A 5 ft < D 2 < 20 ft 
• 20 ft < D 2 < 40 ft 
O 40 ft < Z) 2 < 80 ft 
A 80 ft < Z) 2 < 300 ft 


on Figure 29; the upper is to be compared with the 
curves 3, 4, and 5 of Figure 14 and lies well below all 
three. The lower curve corresponds to curves 1 and 2 
of Figure 14; it lies between them at all except the 
shortest ranges. It should be noted that the special 
projector was used for the 60-kc work in order to 
make certain that the differences between Figure 14 


THE TRANSMISSION OF SUPERSONIC HORIZONTAL BEAMS 


43 


RANGE, YD 



Figure 30. Dependence of transmission anomaly on 
hydrophone depth for 60-kc sound. Negative surface 
gradients Z) 2 < 5 ft. Curve 1 — shallow hydrophone; 
Curve 2 — deep hydrophone. Compare with Figure 15 
for 24-kc sound. 

and Figure 29 were not due to beam-pattern effects. 

It may be concluded that the transition from good 
to bad transmission conditions is more abrupt at 60 
kc than at 24 kc, and that good conditions at 60 kc 
are quantitatively equivalent to fairly poor condi- 
tions at 24 kc. 

In the same way, Figures 30 and 31 should be 
roughly comparable to Figures 15 and 17. There are 
slight differences in the thermal conditions and 
hydrophone depths used in separating the data into 
classes before averaging. It is thought that this does 
not appreciably affect the comparison. It is seen that 
the dependence of transmission anomaly on hydro- 
phone depth is qualitatively the same at 60 kc and at 
24 kc. Under conditions of marked downward re- 
fraction, the effect may possibly be somewhat smaller 
at 60 kc. Under good thermal conditions, the average 
attenuation coefficients at 60 kc are 13.5 X10 -3 
db/yd for hydrophones above the thermocline, and 
16.5 X 10 -3 db/yd for hydrophones below the ther- 
mocline. The corresponding values for 24-kc sound 
are 4.0 and 6.7 X 10 -3 db/yd. Within the limits of 
error, the layer effect (difference between the two 
coefficients) is the same at the two frequencies. 

3.2.8 Transmission of 24-kc Sound When 
Both Projector and Hydrophone Are Deep 

The study of the transmission of supersonic sound 
at greater depths will probably yield information 
concerning the causes of various phenomena. Speci- 
fically, if both source and receiver are deep enough, 
the time delay between the direct and surface-re- 
flected sound is great enough to resolve the two 
pulses and thus to obtain more information on each. 


RANGE, YD 



Figure 31. Dependence of average transmission 
anomaly on hydrophone depth for 60-kc sound. Iso- 
thermal surface layer. D 2 < 40 ft. Curve 1 — hydro- 
phone above thermocline; Curve 2 — hydrophone below 
thermocline. Compare with Figure 17 for 24-kc sound. 

Experiments with deep projectors transmitting 
24-kc sound were carried out in the summer of 
1945. 20 The projector was lowered to depths of 150 ft, 
300 ft, 500 ft, and 1,000 ft. In addition, a few runs 
were made with the source at 16 ft for comparison. 
The signals were received on three hydrophones: 
one always at 16 ft, a second at the projector depth, 
and a third at some other of the stated depths. 

Oceanographic conditions during the experiments 
were such as to produce negative gradients near the 
surface. The thermal structure at depths greater than 
400 ft could not be determined with the bathy- 
thermographs available at the time. 

A small amount of data was accumulated, but the 
completion of the project was deferred by the pres- 
sure of more urgent work and by the need of a more 
suitable transducer. The available data appear to 
warrant some tentative conclusions. 

In Figure 32 are shown average anomaly curves 
for three projector depths, 150 ft, 300 ft, and 1,000 
ft. The hydrophone was at the same depth as the pro- 
jector. These curves are not intended to provide the 
complete information obtained but merely to illus- 
trate the conclusions that have been drawn from a 
study of all data. 

1. Down to a depth of 300 ft, transmission im- 
proves as the projector is lowered. At 150-ft depth, 
Figure 32 shows that the anomaly increases 26 db 
out to 2,000 yd, whereas at 300-ft depth the anomaly 
has increased only 7 db at the same range; at 1,000-ft 
depth the increase is about 5 db, very nearly equal, 
considering experimental error, to the increase at 
300 ft. 

The results agree with deductions from ray theory. 
The shadow boundary extends to greater ranges at 
greater depths (see Figure 17 of Chapter 2), and one 


44 


THE TRANSMISSION OF SOUND IN THE SEA 


RANGE, YD 



Figure 32. Average transmission of sound using deep 

projector. Projector depth = d; hydrophone depth =h. 

might expect better transmission at greater depths. 
Moreover, one might expect that this improvement 
would gradually cease as the projector was lowered 
still more, since the refraction effect would tend to 
become constant for all practical ranges as the pro- 
jector depth increased. 

2. The anomaly graphs are seen to be linear and 
thus are similar to curves 4 and 5 of Figure 14, which 
represent transmission conditions near the surface 
where there exists a deep isothermal surface layer. 

This also is to be expected, for below the main 
thermocline the gradients are weak (see Figure 2 of 
Chapter 2). At depths of 500 ft or more it is very 
probable that the refraction of the sound beam con- 
tributes less to the transmission loss at all ranges 
than does absorption, and thus the attenuation would 
approach a minimal value. However, this minimal 
attenuation is still much larger than can be explained 
by theory. This subject is discussed in detail in 
Section 3.4. 

3. In some cases the direct signal is weaker than 
the surface-reflected pulse. The reason for this is not 
known; it may possibly be attributable to refraction 
effects similar to those described in Section 3.1.4 in 
connection with explosive sound. 

4. The direct signal appears to fluctuate less at 
short ranges when the projector is deep. This is not 
true at long ranges, nor was any improvement noted 
in the case of the surface-reflected signal. This point 
will be discussed in Section 3.5. 


3 3 THE TRANSMISSION OF SONIC 
FREQUENCIES 

3 . 3.1 Description of the Experiments 

The transmission of underwater sound of sonic 
frequencies was not studied experimentally in a sys- 
tematic manner until January 1945. In late 1943, 
plans for the cooperative program of the University 
of California and the U. S. Navy Radio and Sound 
Laboratory had been extended to include this phase 
of the general problem of transmission. Delays were 
occasioned by the outfitting of additional vessels 
and the building of a suitable sound source of high 
intensity, as well as other equipment. 

In general, the experiments were similar to those 
with supersonic sound, already described. The tech- 
nique of simultaneous transmission of several fre- 
quencies was extended, provision being made for the 
simultaneous use of 0.2, 0.6, 1.8, 7.5, and 22.5 kc. 
The supersonic frequency of 22.5 kc was included 
to facilitate comparison with the 24-kc experiments 
previously carried out. It was possible to record all 
five of these frequencies oscillographically on a single 
strip of paper. Alternatively, any one or more of 
the frequencies could be omitted and the remainder 
received on several hydrophones each, thus en- 
abling the observer to compare simultaneous meas- 
urements at any particular frequency. However, 
the maximum number of simultaneous records was 
limited to five. 

The logging of such complex operations presented 
formidable problems which were overcome by the 
use of various automatic recording devices. After 
the program was well under way, data were accumu- 
lated at such a rate that the available office staff 
was barely able to cope with the routine aspects of 
its analysis. The possibility of constructing special 
computing machines to facilitate this work was 
considered but has not been put into effect at the 
date of this writing. 

As a result of these experiments, it has been found 
that two major qualitative differences exist be- 
tween the transmission of horizontal supersonic 
beams and the transmission of the spherical waves 
of lower frequencies. In the first place, the image 
effect, the general nature of which has already been 
discussed in connection with explosive sound, as- 
sumes a much greater importance in the transmission 
of sonic frequencies than in that of supersonic. In 
the second place, much more sound is reflected from 


THE TRANSMISSION OF SONIC FREQUENCIES 


45 


the bottom even in deep water, since the sources of 
sonic sound are relatively nondirectional. 


described in Section 3.2 that led to equation (6); 
a generalization of equation (6) is 


3 . 3.2 Theory of the Surface-Image Effect 

The phenomenon called the “image effect,” as 
encountered in the study of explosive sounds, was 
described in Section 3.1: The waves that are trans- 
mitted directly arrive at a slightly earlier time than 
the waves that have been reflected by the surface. 
The sound emitted by a projector, however, differs 
essentially from that of an explosion: the latter 
consists of a single compression, whereas the former 
is a sinusoidal wave train and consists of an alterna- 
tion of compressions and rarefactions. This intro- 
duces interference, which is, in principle, similar 
to that described in Section 3.2.5 in connection with 
the bottom echo. We shall proceed to calculate the 
effect of the interference of the surface reflection 
on the transmission anomaly. 


I = P 2 (1 — 2(jl cos 27 rf A t + P 2 )- ( 9 ) 


Equation (9) can be put into a more convenient 
form by using the expression for At derived in 
equation (3), 


2 hd 

At = 

rc 


(3) 


and by introducing a parameter R, defined by 


R = 4hd 



4 hd 
X 


( 10 ) 


where X ( = c/f) is the wavelength of the sound, in 
the same units as h and d. 

Multiplying equation (3) by / and using equa- 
tion (10), 


2 fhd R 

fAt = — — = — , 
cr 2 r 


(id 


The Image Effect and the Transmission 
Anomaly 

The pressure in the direct wave is given by the 
equation 

Pi = P cos 2 t rft, (7) 

where P = the amplitude of the pressure variation, 
/ = the frequency of the sound, 
t = the time. 

The pressure p 2 in the wave reflected from the 
surface will be given by an equation similar to 
equation (7). However, the sound reflected from the 
surface will be delayed by a time interval At. 
Moreover, the amplitude of the wave will be differ- 
ent after reflection: if the surface reflects the fraction 
M of the sound energy incident on it, the amplitude 
of the reflected wave will be nP. (The fraction /z is 
known as the effective reflection coefficient of the 
surface.) Finally, the wave suffers a change of phase 
when reflected from the surface, as was shown by 
the explosion experiments described above. This 
reverses the sign of the equation. Thus the pressure 
in the reflected wave will be given by 

p 2 = — nP cos 27 rf ( t — At). (8) 

The resultant intensity I of the direct and re- 
flected waves can be calculated by the methods 


and substituting this in equation (9), we get 

I (i tR\ 

- = 1-2 M cos (-J+M 2 (12) 

It can be shown that, when this interference 
between surface echo and direct sound occurs, the 
mathematical expression for the transmission anom- 
aly is 



= — 10 log j^l — 2 n cos ^ ^ (13) 

Graphs of A as a function of r/R for several 
values of the surface-reflection coefficient ju are shown 
on Figure 33. The curves have been displaced ver- 
tically by arbitrary amounts in order to avoid 
confusing intersections. 

It is seen that the curves have alternate maxima 
and minima; these occur as the cosine takes its 
extreme values of ± 1 and are given by the equation 

A = — 20 log (1 ± ff) (14) 

at values of the range 

R R 

r = R, — , — , etc. 

2 3 




46 


THE TRANSMISSION OF SOUND IN THE SEA 


r/R 



Figure 33. The image effect as a function of r/R, for various values of the surface-reflection coefficient n. The 
curves have been displaced vertically by arbitrary amounts to avoid confusing intersections. 


The range to the last maximum is R, which, as seen 
from equation (10), is determined by the depth of 
projector and hydrophone and varies inversely as 
the wavelength x of the sound. This particular 
critical value of the range is called the Lloyd range, 
after Humphrey Lloyd, who first studied the anal- 
ogous optical effect, which is generally called the 
Lloyd mirror effect. (Other names are the image 
effect, which has been used here, the double-source 
effect, and the dipole effect.) 

Effect of Refraction on the Image Effect 

While it has been assumed that there is no curva- 
ture of the sound rays, it may be anticipated that 
the equations will be valid provided the refraction 
is not too great. Thus, in the case of downward 
refraction, it should be sufficient that the Lloyd 
range be much less than the range to the shadow 
boundary at the hydrophone depth. Departures will 
be expected whenever the Lloyd range becomes 
comparable to the latter. 


A more careful consideration of this matter leads 
to Table 1. In preparing this table, it was assumed 
that hydrophone and source are both at the depth 
d ( = h), and AT is the temperature difference be- 
tween the surface and the depth d (regardless of 
sign). The tabulated values AT are the largest for 
which the above equations should be valid. For 
convenience, the values of R corresponding to the 
tabulated values of frequency and depth are also 
tabulated. 

It is seen that, for very low frequencies, the Lloyd 
range is so short that the equations should be 
valid for almost any thermal conditions that are 
apt to occur in the ocean. For frequencies above 
5 kc, on the other hand, it is very unlikely that they 
will ever be applicable without modification except 
when the projector and hydrophone are at very 
shallow depths and short ranges. 

Figures 34, 35, and 36 show a comparison between 
this theory and experimental data for 200, 600, and 
1,800 c. The arrows indicate the Lloyd range; its 
increase with frequency is apparent. The curves 


THE TRANSMISSION OF SONIC FREQUENCIES 


47 


Table 1. Maximum values of AT for which equation 
(13) is valid. 


Fre- 







quency 

d = h = 

= 16 ft 

d = h = 

= 35 ft 

d=h 

= 90 ft 

(c) 








R( yd) 

AT(°F) 

R( yd) 

AT(°F) 

R( yd) 

AT(°F) 

100 

7 


34 


225 

15 

500 

35 

20 

170 

4 

1,125 

0.6 

1,000 

70 

5 

340 

1 

2,250 

0.15 

5,000 

350 

0.2 

1,700 

1.04 

11,250 

0.006 

10,000 

700 

0.05 

3,400 

0.01 

22,500 


24,000 

1,700 

0.008 

8,150 


54,000 



RANGE, YD 


,U 2 3 5 100 2 3 5 1,000 2 3 5 iqOOQ 




• 

• 

'S; 

>URFA< 
w. U 

ZE 
L= 1 

IMAC 

JE 











L. 











• 

• I 

• 

• • 

• • 

• 

M 





• EXPERIMENTAL 
— THEORETICAL 
f =0,2 KC 

OCEAN DEPTH-2000 FM 

Hydrophone depth so ft 








Figure 34. Theoretical and observed transmission of 
sound in deep water. Frequency 0.2 kc. 


RANGE, YD 



Figure 35. Same as Figure 34 for 0.6-kc sound. 


RANGE. YD 



Figure 36. Same as Figure 34 for 1.8-kc sound. 


have been plotted for values of ix chosen to give the 
best fit. In agreement with Table 1, no data for 
higher frequencies conform to these equations. 

The manner in which refraction should modify 
the image effect is shown by Figure 37. 3 The solid 
curve has been calculated for the case of downward 
refraction, projector and hydrophone being at a 
depth of 20 ft and the range to the shadow boundary 
being 2,200 yd. For comparison, the dotted curve 

RANGE, YD 


10 20 30 50 100 1000 10000 



Figure 37. Image effect with slight downward refrac- 
tion. Frequency 1,000 c, /* = 1. The arrow indicates the 
range of the last maximum. 


shows the effect in the absence of refraction. The 
curves are drawn for n = 1 and 1,000 c. They show 
that refraction displaces all the maxima toward 
shorter ranges and that the sound level should in- 
crease at ranges just short of the shadow. This last 
effect is caused by the diminished time delay of the 
surface echo (see Figure 5), together with the in- 
creased divergence of the reflected rays. 

It may be anticipated that this theory will be 
valid at short ranges, but it is likely that diffraction 
and other neglected phenomena will greatly modify 
the anomaly curve near the shadow. 

The effect of increased refraction will be to move 
the shadow boundary toward shorter ranges and to 
compress the curve still further. The effect of in- 
creased frequency will be to move the maxima 
toward longer ranges, the shadow boundary remain- 
ing fixed. 

At short ranges, the image effect is modified 
because the source and its image are not at the same 
distance from the surface. This and other effects 
have been investigated theoretically, and partially 
confirmed by experiments. 4 The data of one experi- 
ment are compared with theory in Figure 38. 

One point is brought out by this figure: the 
intensity of the sound is not constant but fluctuates 




48 


THE TRANSMISSION OF SOUND IN THE SEA 


RANGE, FT 



Figure 38. Power-level recorder trace showing the image effect at very close ranges. This figure is a photograph of 
the original trace; the solid curve was drawn in and shows the theoretical image effect. The two are seen to check 
fairly well. 


rapidly in an unpredictable manner. Something of 
the nature of these fluctuations can be seen in 
Figure 23, which shows details of the interference 
between sounds arriving by two paths. The great 
variability of the complex signals is, in that case, 
probably caused by a combination of effects that 
include pitching and rolling of the ship, local ir- 
regularities in the bottom topography, and local 
variations in the velocity of sound. In the case of 
Figure 38, the changing shape of the sea surface is 
another cause. Fluctuation of transmission is dis- 
cussed in detail in Section 3.5. 

When these fluctuations become extreme, one is 
reduced to considering only average values. These 
average values are not influenced by interference 
and can be calculated simply by adding the in- 
tensities of the sounds arriving by different paths, 
without regard to the phase relations. 

3.3.3 Theory of Bottom Reflection 

There are many ways in which sound can reach 
the hydrophone from the projector. A few of the 
most important of these are shown in Figure 39. 
They are 


PH 

Direct 

PSH 

Surface reflected 

PBH 

Bottom reflected 

PS 1 B 1 H 

PB 2 S 2 H 

ps 3 b 3 s 4 h 

Multiply reflected 


There are additional paths involving several reflec- 
tions from the bottom as well as several from the 
surface. 

A complete theory of sound transmission would 
involve a consideration of all the infinite variety of 
paths, together with their modification by refrac- 
tion. 5 Fortunately, the sound arriving via most of 


s 3 s, s s 2 s 4 



Figure 39. Diagram illustrating reflection from the 
surface and the bottom, and showing some of the rays 
along which sound may travel between projector and 
hydrophone. 

the paths is usually negligible, so that only a 
small number of them need be considered at any 
one time. The problem can be made simpler as 
follows. 

1. If a narrow beam is sent out horizontally in 
deep water, very little sound will be emitted along 
rays that reach the bottom at reasonable ranges. If 
a nondirectional projector sends out a short pulse, 
the reflected sound traveling along PBH may arrive 
so much later than that going directly via PH that 
the two pulses are easily distinguished. Under either 
of these circumstances only the two paths, PH and 
PSH, need be considered. These are involved in the 
surface-image effect, which has been discussed in 
Sections 3.1.2 and 3.3.2. 

2. If a projector sends out long pulses, the 
possibility of distinguishing the direct from the 
bottom-reflected sound is lost, and under certain 
conditions, the latter may be the more intense. Thus 
there will be interference between the two pulses. 
This effect was discussed in Section 3.2.5. 

3. When both hydrophone and projector are near 
the surface, and the water is very deep, the four 
paths, PBH, PSiBiH, PB 2 S 2 H, and PS.BzSiH, will 
not differ greatly in length. If, in addition, the 



THE TRANSMISSION OF SONIC FREQUENCIES 


49 


sound frequency is low, the waves arriving by these 
four paths may interfere, producing effects analogous 
to but more complex than the surface-image effect. 
Calculations of the expected effects have been made 
and receive some confirmation from experimental 
data. 10,11 In general, however, the fluctuations dis- 
cussed at the end of the previous section will be so 
great as to obscure the details of the interference 
pattern. It is then sufficient to calculate the average 
intensity resulting from the four paths. This can be 
done crudely by calculating the intensity of the 
sound arriving via PBH and multiplying it by four. 
If the water depth is comparable to the horizontal 
distance between P and H , a further simplification 
is possible, for the rays PB and BH are then inclined 
so steeply to the horizontal that all refraction effects 
can be neglected. 

With these simplifications, the length of the path 
is approximately 

PBH = (r* + 4s 2 ) J , (15) 


r /s 


0,1 1.0 10 100 



RATIO OF TRAVEL DISTANCE TO WATER DEPTH 


Figure 40. Graphs of the equation a = 10 log (& 2 /r 2 + /4) 
—20 log n for various values of f. The value of is 
given by 

1 — f cos 0 

n= 

1 +f cos 0 

when 0 is the angle of incidence and is given by tan 
0=r/2&. On the figure both 0 and r/S are indicated 
as abscissas. 


where r = PH and s is the depth of the bottom below 
the projector or hydrophone. (The difference in 
their depth is neglected.) The total intensity of the 
bottom-reflected sound arriving over all four paths 
can then be calculated from the inverse square 
law to be 


4/pu 2 
r 2 + 4s 2> 


(16) 


where Ii = intensity at unit distance from the source, 
fi being the amplitude-reflection coefficient of the 
bottom. The transmission loss is therefore 

H =10 log (y) 

= 10 log (s 2 +\r 2 ) — 20 log fi, (17) 

and the transmission anomaly is 
A = H — 10 log r 2 

= 10 log jyj +yj - 20 log IX. (18) 


but changes with the angle 0 at which the sound is 
reflected from the bottom. This angle is given by 

tan 0 = — . (19) 

2s 


The value of 0 corresponding to a given value of r/s 
is shown by the upper scale of Figure 40. 

There are no good data on the manner in which 
the reflection coefficient varies with 0. One equation, 
based on the concept of acoustic impedance, is 


M = 


1 - f cos 01 
.1 + f cos 0J 


(20) 


where f is the acoustic impedance of the bottom, 
measured in units of the acoustic impedance of 
water. lb From equation (20), if f = 0, /* = 1; curves 
of A for f and f = 1, are also shown in Figure 
40. Other theoretical equations for n would yield 
curves of slightly different shapes. 


The Effective Reflection Coefficient 


The upper curve of Figure 40 shows this equation 
for /z = 1 . If ii has any other constant value less than 
unity, the whole curve will be shifted downward 
without altering its shape. However, there are the- 
oretical reasons for supposing that /z is not constant, 


It would be expected that the effective reflection 
coefficient /z would decrease as the sea’s surface 
becomes rougher. This effect, if it exists, is obscured 
by the large uncertainty in the value of /z determined 
by the method of best fit. It would also be expected 


50 


THE TRANSMISSION OF SOUND IN THE SEA 


that m would decrease with increasing frequency. 
This may be an additional reason why the image 
effect is not observed at higher frequencies. Two 
samples of data on this effect are shown in Table 2; 

Table 2. Distribution of effective reflection coefficients 
of the sea surface. 


Number of observed cases 



20 c 

600 c 

1,800 c 


W-Sp 

Su 

W-Sp 

Su 

W-Sp 

Su 

1.0 

7 

20 

3 

20 

1 

12 

0.8 

4 

0 

7 

2 

3 

4 

0.5 

0 

0 

16 

1 

16 

0 

0.1 

0 

0 

0 

0 

4 

0 

No fit 

3 

0 

3 

0 

4 

4 


one sample taken in winter and spring, the other 
in the summer. The latter sample, in general, shows 
higher values of /x, perhaps because the sea surface 
is smoother in summer. 

3.3.4 An Example of the 

Simultaneous Transmission of 0.2- and 
22.5-kc Sounds 

Figure 41 presents the data obtained during an 
unusually long transmission experiment, in which 

RANGE, YD 

100 1000 10000 



Figure 41. Transmission of 200-c sound, for ranges 
from 60 yd to 60,000 yd. Theoretical curves for direct 
and surface-reflected sound (r ^ 1,000 yd) and for 
bottom-reflected sound (r ^ 1,000 yd) are shown. Pro- 
jector depth = 14 ft. Hydrophone depth =50 ft. Iso- 
thermal surface layer approximately 75 ft deep. 
Average ocean depth 2,000 fathoms. 

the range was opened from 60 yd to more than 
60,000 yd. At ranges less than 1,000 yd, the sound 


was received via the paths PH and PSH, and its 
intensity is governed by the equation (18) with 
ix = 1 , as shown by the smooth curve. At ranges 
greater than 1,000 yd, the sound was received via 
bottom reflection. This was established by compar- 
ing the arrival time with that calculated from the 
range; the latter was determined by radar or radio- 
acoustic ranging with 22.5-kc sound, or both. The 
smooth curve for ranges greater than 1,000 yd is 
taken from Figure 40 for £* = 0.5; it is probable that 
£ = 0.6 would have fitted the data more closely. The 
irregular fluctuation of the bottom-reflected sound 
is apparent from the scatter of the experimental 
points. 

The sound frequency was 200 c, the projector 
depth 14 ft and the hydrophone depth 50 ft. There 
was an approximately isothermal layer about 75 ft 
deep at the surface of the sea. The water depth was 
not constant over the whole range, but averaged 
about 1,000 fathoms. The 200-c sound received on 
a hydrophone at 300 ft showed much the same 
variation with range, although the quantitative 
agreement with the theory was not so good. 

For comparison, Figure 42 shows the transmission 
of 22.5-kc sound to the 50-ft hydrophone from a 
projector at 12-ft depth. The data for Figures 41 and 


RANGE, YD 

100 1000 10000 



Figure 42. Transmission of 22.5-kc sound obtained 
simultaneously with that of Figure 41. Theoretical 
curve showing image effect drawn for comparison. 
Projector depth = 12 ft. Hydrophone depth =50 ft. 

42 were obtained simultaneously. At ranges less than 
100 yd, the directivity of the 22.5-kc projector causes 
a large anomaly. At ranges from 300 to 3,000 yd, 
the 22.5-kc anomaly is less than the 0.2-kc anomaly 
and is unusually small compared to the average of 
the 24-kc runs (see Figure 14). Beyond 3,000 yd, 


THE TRANSMISSION OF SONIC FREQUENCIES 


51 


the anomaly of the 22.5-kc sound increases rapidly, 
and, because of the directivity of the source, there 
is no measurable bottom-reflected sound. The graph 
of the surface-image effect for n = 1, and neglecting 
refraction, is included for comparison. 

3.3.5 The Influence of Hydrophone 
Depth on the Transmission of Low-Frequency 
Sound — Layer Effect 

The discussion of the average values of the trans- 
mission anomaly at low frequencies is simplified by 


points obtained under similar thermal conditions are 
plotted with different symbols. The data have been 
classified according to D 2 . The expression d 2 — 2 in- 
dicates that D 2 was between 10 and 20 ft; d 2 = 3 
indicates the range 20 to 40 ft; d 2 = 4, 40 to 80 ft; 
d 2 = 5, 80 to 160 ft, and so forth, according to the 
code described in Section 2.1.5. The averages for 
these different classes show some differences but 
they are usually not greater than the sampling error, 
and when they are greater, they do not appear to 
be systematic. 

It is quite possible that some other classification 
based on thermal conditions would reveal more sys- 


RANGC, YD 




Figure 43. Comparison of simple theory with data of an experiment in transmission of 0.2 kc, with shallow hydro- 
phone, for d 2 = 2 and d 2 = 4. The light solid curve represents constant level. 


the fact that thermal conditions near the surface do tematic differences. The discovery of this method 
not greatly influence them. In Figures 43 to 48, in- of classification, if it exists, must await further data 
elusive, the averages of five to twelve experimental and analytic work. 




52 


THE TRANSMISSION OF SOUND IN THE SEA 


RANGE , VD 




Figure 44. Same as Figure 43, but with deep hydrophone. 


The data at 0.2, 0.6, and 1.8 kc are adequately 
explained by the combination of surface and bottom 
reflection. This is indicated by the solid curves, 
which represent the theoretical graphs of these 
effects, neglecting refraction. In every case, the 
bottom reflection is in fair agreement with the 
theoretical curve for bottom impedance f = 0.5. The 
data for the 16-ft hydrophone (Figures 43, 45, 47) 
agree well with the theory of the surface-image 
effect for reflection coefficients of 0.8 to 1.0. The 
data for the 300-ft hydrophone (Figures 44, 46, 48) 
show systematic departures which are, however, 
precisely of the kind to be expected from the effects 
of refraction in the deep layers. (See Figure 37.) 
Some of the average curves even show some of the 
maxima and minima of the surface-image interfer- 
ence, but they are displaced to ranges shorter than 
those predicted by the simple theory. (See the broken 
lines of Figures 46 and 48.) 


This general agreement with simple theory is very 
gratifying, and holds promise for quantitative im- 
provement when the theory has been elaborated to 
include the effects of refraction. 

As of the date of writing, the data on the trans- 
mission of 7.5-kc sound do not lend themselves to 
presentation in summary graphs. There are good in- 
dications that these will be intermediate between 
those presented here for 24- and 60-kc sound, on the 
one hand, and those for 0.2, 0.6, and 1.8 kc on the 
other. The values of the transmission anomaly are 
probably markedly dependent on the depth at which 
the first perceptible decrease of temperature occurs. 
There is also some indication that conditions at 
greater depths have an influence. Bottom-reflected 
sound is less prominent, since the 7.5-kc projector 
is somewhat directional. The maxima and minima 
of the surface-image effect are, to say the least, not 
obvious. 




ANOMALY, DB ANOMALY, DB ANOMALY, DB 


THE TRANSMISSION OF SONIC FREQUENCIES 


53 





Figure 45. Same as Figure 43, for three different thermal conditions, with sound of 0.6 kc, using shallow hydrophone, 





ANOMALY. OB ANOMALY. OB ANOMALY. OB 


54 


THE TRANSMISSION OF SOUND IN THE SEA 


RANGE, YD 





Figure 46. Same as Figure 45, but with deep hydrophone. 




THE MINIMAL ATTENUATION COEFFICIENT 


55 


RANGE, YD 




3.4 THE MINIMAL ATTENUATION 
COEFFICIENT 

3 .4 i Causes of Attenuation 

It has been shown (Section 3.2) that, under the 
most favorable conditions, the transmission anomaly 
can be represented by an equation of the form 

A =ar (4) 

where a is an empirical constant called the attenu- 
ation coefficient. It was shown further that under less 
favorable conditions this simple equation completely 
fails to represent the facts. 

The physical significance of equation (4) is that 
energy is removed from the beam in amounts that 
are proportional to the total energy in the beam. 
Under favorable conditions, i.e., when there is no 
refraction and the sound rays are straight, there 
are two general ways in which this will happen : 


1. A certain fraction of the sound energy is con- 
verted into heat energy. This is called absorption . 

2. Another fraction of the sound energy is deflected 
from its original path by obstacles suspended in the 
medium and thus is removed from the beam. This 
is called scattering. 

Absorption in turn is caused by at least three 
processes : 

1. The viscosity of the medium causes sound 
energy to be converted into heat by internal friction. 

2. Thermal conduction : some sound energy is 
converted into heat because sound waves alternately 
raise and lower the temperature by very small 
amounts. 

3. Suspended particles are set to oscillating by 
the sound waves and in this process some of the 
sound energy is dissipated in the form of heat. This 
is especially the case if the particles are air bubbles. 




56 


THE TRANSMISSION OF SOUND IN THE SEA 


RANGE, YD 





The effects of scattering cannot be readily isolated 
from those of absorption, but the theories of scatter- 
ing and absorption are rather different. These three 
processes are not all of equal importance in the sea. 


According to calculation, viscosity is more import- 
ant than thermal conduction and scattering com- 
bined. It is possible that the effect of bubbles is 
important, but this has not been proved. Because of 



THE MINIMAL ATTENUATION COEFFICIENT 


57 


the complex mathematics involved in its discussion, 
no detailed treatment will be given here. 7 * 22,23 (See 
Section 3.4.2 below.) The attenuation due to scat- 
tering will be considered in Chapter 5. 

3.4.2 The Attenuation Caused by Viscosity 

The theory of absorption due to viscosity was 
first given by Kirchhoff, and is reproduced in most 
standard textbooks. 2b The result is that 

167T 2 77/ 2 

a = logioe db per unit length, (21) 

3 pc 3 

where t] = coefficient of viscosity of medium, 

/ = frequency of sound, 
p = density of medium, 
c = velocity of sound. 

Substituting the values of 77 , p, and c appropriate to 
sea water at 65°F, and expressing / in kc, 

a = 6.8 p X 10- 5 db/yd. (22) 

A similar numerical expression can be obtained for 
fresh water. Laboratory experiments indicate that, 
at frequencies above several hundred megacycles, 
this equation gives the proper order of magnitude 
of the attenuation coefficient but is in error by a 
factor of 2 or 3. 19a A possible explanation of this 
error has been suggested. 12 At lower frequencies, the 
observed attenuation is very much greater than that 
to be expected from viscosity. 

This is shown by Figure 49, in which the ratios 
of the experimental values of a to those given by 
equation (21) are plotted against the frequency in 
kilocycles. The dotted curve, for fresh water, is taken 
from Reference 7. The solid curve is taken from Fig- 
ure 50. It is seen that for frequencies less than 
1,000 kc, all measured attenuations are more than 
10 times greater than can be caused by viscosity. In 
the 10- to 100-kc range, the attenuation in the sea 
is 40 to 200 times greater than that resulting from 
viscosity, but is still several hundred times less than 
would be expected from an extrapolation of the curve 
for fresh water. 

A possible explanation for the large attenuation 
was proposed by H. F. Willis, who suggested that it 
could be ascribed to the absorption caused by the 
suspension of very small air bubbles in the water. 
Laboratory experiments with ordinary and air-free 
water do show a difference, but it is not great enough 
to explain the facts of Figure 49. Further experi- 
mental research in this field is urgently needed. Such 


FREQUENCY, KC 


10 IQ* 10* IQ 4 I o 5 




\ 





\ 

\ 





\ 



TRANSMISS 
AT SEA 

.ionX 

t — 

\f 

RESH WATI 

:r 


’LABORATORY 

'measurements 




^ ( F ROM REI 

r 7) 









\ 

\ 





\ 

\ 





\ 

\ 













Figuee 49. Ratio of experimental values of A to those 
given by equation (21), for both fresh water laboratory 
measurements and transmission at sea. 


FREQUENCY, KC 



tion coefficients listed in Table 3 (taken from Reference 
12, revised to 1945). The meaning of the symbols is 
given in Table 3. 

large discrepancies cannot be ascribed to experi- 
mental error, and theoretical speculation appears un- 
able to suggest a completely satisfactory explanation. 


58 


THE TRANSMISSION OF SOUND IN THE SEA 


3.4.3 The Minimal Attenuation Coefficient 
Definition 

The attenuation observed in the transmission ex- 
periments differs from that caused by viscosity in 
another important respect. The latter coefficient 
should be quite independent of thermal gradients, 
although it might be obscured by the effects of re- 
fraction. The values of the observed attenuation, on 
the contrary, depend markedly on the temperature 
gradient in the upper layers (see Figure 14) and 
decrease a s the gradients diminish. a In order to have 

a An exception to this rule occurs when both negative and 
positive gradients are present, forming a sound channel 
(see Section 2.3.3). The exceptionally low values of the trans- 
mission loss under these conditions is adequately explained 
by refraction theory. They are therefore excluded from con- 
sideration in the following paragraphs. 


a single definite value for the observed attenuation 
coefficient, only the values observed when the tem- 
perature gradients in the upper layers are small and 
negative have been considered. For want of a better 
term, these values have been called the minimal 
attenuation coefficients and are designated by a Q . 
It is probable that these values approximate the 
attenuation that would be observed in an isothermal 
ocean. 


Observed Values 

Observed values of the minimal attenuation co- 
efficients are listed in Table 3 and plotted on Figure 
50. The table and figure are taken from a report, 12 
revised to 1945. They summarize the measurements 
made at sea in the frequency range 10 to 100 kc. 


Table 3. Minimal attenuation coefficients. 


Freq. (kc) 

Minimal 
atten. coeff. 

(10 -3 db/yd) 

Location 

Method 

Experimenters 

Figure 50 
symbol 

18 

1.8 

S. Atlantic and 






Caribbean 

Ship-to-ship 

NRL Ref. 16 

Solid triangle 

24 

4.4 

S. Atlantic and 






Caribbean 

Ship-to-ship 

NRL Ref. 16 

Solid triangle 

30 

6.5 

S. Atlantic and 






Caribbean 

Ship-to-ship 

NRL Ref. 16 

Solid triangle 

18 

3.4 

Off Panama 

Ship-to-ship 

NRL Ref. 16 

Solid triangle 

24 

4.8 

Off Panama 

Ship-to-ship 

NRL Ref. 16 

Solid triangle 

14 

2.5 

Off San Diego 

Ship-to-ship 

UCDWR Ref. 12 

Open triangle 





and later work 


24 

4.5 

Off San Diego 

Ship-to-ship 

UCDWR Ref. 12 

Open triangle 





and later work 


56, 60 

15.0 

Off San Diego 

Ship-to-ship 

UCDWR Ref. 12 

Open triangle 





and later work 


24 

4.7 

Off Pt. Conception 

Ship-to-ship 

UCDWR Ref. 12 

Open triangle 





and later work 


20 

1.8 

San Diego Harbor 


UCDWR Ref. 17 

Solid Square 

40 

6.5 

San Diego Harbor 


UCDWR Ref. 17 

Solid square 

60 

16.5 

San Diego Harbor 


UCDWR Ref. 17 

Solid square 

80 

24.0 

San Diego Harbor 


UCDWR Ref. 17 

Solid square 

100 

29.5 

San Diego Harbor 


UCDWR Ref. 17 

Solid square 

20 

4 ± 1 

Off San Diego 

Vertical pulse 

UCDWR Ref. 17 

Open circle 

25 

3 ±2 

Off San Diego 

Vertical pulse 

UCDWR Ref. 17 

Open circle 

40 

11+2 

Off San Diego 

Vertical pulse 

UCDWR Ref. 17 

Open circle 

60 

16 + 2 

Off San Diego 

Vertical pulse 

UCDWR Ref. 17 

Open circle 

100 

22 ±1 

Off San Diego 

Vertical pulse 

UCDWR Ref. 17 

Open circle 

10 

1.2 

? 

? 

British 

Solid circle 

60 

15 




Solid circle 

300 

300 





24 

3.0 

Off San Diego 

Deep projector 

See Sect. 3.2.8 

Cross 




and hydrophone 




THE MINIMAL ATTENUATION COEFFICIENT 


59 


Vertical Pulsing 

The method of ship-to-ship transmission of pulses 
is rendered difficult by the rarity of suitable thermal 
conditions in inshore water (see Chapter 4). This 
difficulty could be overcome by transmitting sound 
vertically through the ocean, since refraction does 
not affect vertical sound rays (see Chapter 2) and 
presumably the transmission anomaly under these 
conditions will be given by equation (4). However, 
the shallowness of most inshore waters then material- 
ly restricts the distance r that can be achieved be- 
tween source and receiver. 

Other obvious experimental difficulties also arise 
when transducers are to be operated at very great 
depths. These have been avoided by using echo- 
sounding gear and studying the intensity of the bot- 
tom echo produced when the sound beam is directed 
vertically downward. 

A somewhat oversimplified theory of echo sound- 
ing will be given as a basis for discussing the experi- 
ments. If the bottom of the sea were perfectly flat, 
the echo would appear to come from a virtual image 
source, located as far below the bottom as the actual 
source is located above the bottom. If the actual 
distance from source to bottom is s yd, the trans- 
mission loss should be 

H = 2a 0 s — 20 log (2s). (23) 

If the bottom were also a perfect reflector, the 
difference Li — E between the source level L and the 
level of the echo E would be H. However, the bot- 
tom is not a perfect reflector, so that the effective 
source level of the image will be less than L h say L/. 
If n (<1) is the amplitude-reflection coefficient of 
the bottom, 

U = L X + 20 log /x, (24) 

and 

2s 

Li — E = 2 a Q s — 20 log — . (25) 

This is a single equation which contains the two 
unknowns a Q and /x. Both can be determined, pro- 
vided measurements can be made in water of different 
depths over bottoms having the same value of n. 

The procedure actually followed was to make a 
series of measurements over mud bottom, in the 
hope that this would insure the constancy of the 
reflection coefficient. As a test of this assumption, 
the values of 

(26) 


were plotted against 2s. The result is shown in Figure 
51. If n is constant, the graph for any one frequency 
should be a straight line, the slope of which is a 0 
db/yd and the intercept at s = 0 is — 20 log /z. It is 
seen that the points do fall close to the straight 
lines, but there is a possibility that differences in the 

2 S , YD 



Figure 51. Transmission anomaly at various fre- 
quencies as determined by echo-sounding (vertical 
pulsing) experiments. 

reflection coefficient at the various locations have 
influenced the slope of the lines as drawn. In partic- 
ular, the 60-kc line does not appear to be in its 
proper position between those for 40 and 100 kc and 
there is rather more difference between 20 and 25 kc 
than might have been expected. These discrepancies 
may also indicate that the theory outlined above is 
too simple and that the bottom does not behave like 
a mirror under these conditions. 

The vertical pulsing and the ship-to-ship trans- 
mission under good thermal conditions are the prin- 
cipal methods by which values of the minimal at- 
tenuation coefficient have been determined. In addi- 
tion, some measurements have been made in the 
shallow water of San Diego Harbor by transmitting 
pulses from the end of a dock to a small boat, which 
moved along a measured cable. The maximum sep- 
aration between source and receiver in this case was 


A = L 1 -E + 20 log (2s) 


60 


THE TRANSMISSION OF SOUND IN THE SEA 


about 1,000 yd. The effects of surface and bottom 
reflection were pronounced in these experiments, and 
some uncertainty exists as to the necessary corrections. 

3.5 VARIABILITY OF TRANSMISSION LOSS 

3 . 5.1 Changes in Transmission Loss 
with Time 

General Remarks 

In the preceding sections the general empirical laws 
governing the transmission of sound on the average 
have been discussed. Experience has shown that 
departures from the average often have an important 
bearing on many problems, and this is true also of the 
transmission of underwater sound. 

If sound of constant intensity and frequency is 
transmitted through the sea from one ship and re- 
ceived on another at some fixed distance, the re- 
ceived intensity will not be constant. This is very 
apparent when the reception is by ear : the loudness of 
the sound increases and decreases in an easily per- 
ceptible but very irregular manner. The same effect 
is noticed when sound is transmitted several thou- 
sand yards through the open air; it is commonly 
said that the wind “blows the sound away”. A similar 
effect is also known in the transmission of radio 
waves; this is called “fading.” 

The cause of this phenomenon is the changing con- 
dition of the medium through which the sound is 
transmitted. Even though the wind does not literally 
blow the sound away, it does cause changes in the air 
through which the sound must pass, and these in turn 
cause changes in the transmission loss. Similar changes 
occur in the sea, even though the currents are not so 
strong as the wind. The roll and pitch of the ships, as 
well as their steady motion, also contribute to change 
the path of the sound traveling from projector to 
receiver. 

Three Kinds of Time Changes in Signals 

A cursory examination of typical oscillographic 
records of sound transmitted through the sea shows 
the marked variability in the amplitude at a given 
point even during short periods of time. Some typical 
oscillograms of signals received during ship-to-ship 
transmission at various ranges are shown in Figure 
52. These are records of short pings (of 100 msec 
duration) transmitted successively a half-second or a 
second apart. Once each minute a long signal of 10 


sec was transmitted. These long signals are exhibited 
in the upper strips of A, B, and C of Figure 52; the 
bottom halves are records of the short 100-msec 
pings. Strip D is a record of pings received at a range 
of 13 ft and is included for comparison. At this short 
range the signals show very little change. The ray 
diagram at the top shows that the sound recorded 
in A was received in the direct-sound field, and that 
recorded in B and C in the shadow zone. The hydro- 
phone was at 16 ft. 

It is useful to introduce certain terms to describe 
the obvious differences in the oscillograms repro- 
duced in Figure 52. 

Distortion. The amplitude of a short segment of a 
signal will change during a time less than 0.1 sec; 
this will be called distortion. Distortion is especially 
noticeable at long ranges, where the amplitude may 
change by a factor of two or three in 0.05 sec. At 
moderate ranges this factor is considerably less, and 
at 13 ft the effect is practically nonexistent. 

Fluctuation. There are changes in the average 
amplitudes of successive short pings and of successive 
short segments of long pings; this will be called 
fluctuation. It is especially apparent at moderate 
ranges, where there is little distortion. It also occurs 
at longer ranges, but then it is necessary to average 
out the distortion before the fluctuation becomes 
obvious. This average can be found either by in- 
spection or by making a series of measurements and 
computing it arithmetically. 

Variation. Although not shown by Figure 52, there 
are still slower changes in the transmission loss, which 
become appreciable in 15 or 30 minutes. These be- 
come apparent when the average amplitude of a 
number of pings at one time is compared with that of 
another set received at a later time. The range should, 
of course, be constant for both sets. These slow changes 
are called variation. The term variation is also used 
to designate differences in transmission loss measured 
under similar thermal conditions on different days. 

There is no sharp dividing line between these three 
effects, but as they affect practical echo ranging and 
listening in somewhat different ways it is convenient 
to use the terms. 


3 . 5.2 Distortion of Signals 

It is thought that this effect is not very important 
in echo ranging, and consequently it has not been 
studied in great detail. 


VARIABILITY OF TRANSMISSION LOSS 


61 


RANGE, YARDS 

0 200 400 600 800 1000 


TEMP., °F 

55 60 65 



B 


RANGE = 1 700 YD 

r c < « X '* X < (C** : *> *>* * >*''4' *‘XjNf 

,/V ' *• *"• •' ' ■■ ' •" ■ " * ‘ j "'- K ’ '-d 

. "* ■ 'd ~~ .Ni !»«*-«.*■ .■ >« - . ... a .. ■ i«« 









..a .. 


-REVERBERATION- 




RANGE= 4200YD 


PW0< * )».*< s: *•»'>» j fagmimW . ' 0 1 


c 


*4 > 




BACKGROUND NOISE 

RANGE = 13 FT. 


D 


Figure 52. Oscillograms of 24-kc signals received at various ranges during ship-to-ship transmission. The upper 
halves of strips A, B, and C show a long (10-sec) ping; the 100-msec pulses, strip D shows pulses received at 13 feet. 
The bathythermogram and corresponding ray diagram at the top show the sound condition prevailing during the experi- 
ment. Projector and hydrophone depth = 16 ft. Reverberation (forward scattering) and background noise are indicated. 
The increased distortion of the signal at long ranges is clearly seen (UCDWR, San Diego). 


As has already been remarked, the distortion is 
most pronounced at long ranges, where the transmis- 
sion loss is high and the ray theory predicts a silent 
shadow. The small amount of sound received at these 
ranges is probably the result of scattering that occurs 
in the volume or at the bottom of the sea. The sound 
travels along one ray until it reaches some suspended 
obstacle, which becomes a secondary source and re- 
radiates some of the incident sound along other rays. 


This explanation is supported by the fact that the 
distorted oscillograms of Figure 52B and C are very 
similar in appearance to oscillograms of reverbera- 
tion, such as Figure 9 of Chapter 5. Reverberation 
has not yet been discussed but it will be shown to be 
caused by scattering. Further evidence for the valid- 
ity of this explanation of the distortion is to be found 
in the “reverberation tails” indicated on the oscillo- 
grams of the pings in Figure 52B. These indicate that 


62 


THE TRANSMISSION OF SOUND IN THE SEA 


some sound has been en route for a longer time than 
the rest. This is typical of scattering processes, since 
the time required to travel from projector to scatterer 
and thence to receiver depends upon the location of 
the scatterer. Neglecting refraction, this time will be 
least when the three are in the same straight line and 
will increase if the scatterer is out of the direct line. 

At extreme ranges, it is probable that not all of the 
recorded sound originated at the projector. The im- 
possibility of avoiding extraneous noise imposes 
limitations on measurements of this kind. 


3.53 Fluctuation 

Turning our attention to the manner in which suc- 
cessive pings differ from each other, we see from 
Figure 52 that when pings of about 100-msec dura- 
tion are projected at intervals of a few seconds with 
the same amplitude, the average amplitude of one 
ping will, after transmission, differ from the average 
amplitude of its neighbors. This effect is very clearly 
shown by Figure 53A and C, in which the average 
amplitudes of 100 successive signals, received at 
JdJ-sec intervals, are expressed as ratios to the aver- 
age amplitude of all the 100 signals and are plotted 
against time. These fluctuations can be dealt with 
quantitatively by the use of quantities common in 
statistical procedure. Some of these will be discussed 
briefly. 


Standard Deviation 

Let the amplitude of the first ping in a set of N 
pings be x h that of the second ping x 2 , and so on to 
xn . Let the average amplitude of all N pings be x . 
The quantity X\ — x is called the deviation of the first 
ping, x 2 — x, the deviation of the second ping, and so 
on. Two other quantities used to describe fluctuation 
are variance of the set and the standard deviation. 

The variance y is computed by squaring the 
individual deviations and averaging them: 

y=~^ixi-x) 2 +(xi -x) 2 + • • • 

(Xi v- 1 -x 2 ) + (x„-x) 2 J (27) 

The standard deviation o is the square root of the 
variance : 

v =y h (28) 


SUCCESSIVE SIGNALS 




o k - 

A 7 

s IA . A 

\ 

o V 

A 

a. 7 r 

1 v\ l y\ 

\ A / U a i\.. I\ 

, J 

4 /" \.J 

\ J 1 

\ /v 'Ah \. 

V u \ 

c 

yv 

b \ 


CORRELATION INTERVAL, SECONDS 
P 2 4 6 8 10 12 14 16 


2 

0 
h* 

<h 

dS 

SQ 

Ou. 

OU. 

■ UJ ' 

1 O 

00- 

1- 

o . 
< 


v_ 








\ 








. V. 









i 








\ 








\ 

-T>. v 


/ 






\ 


7 

/ 







X 













D 









Figure 53. Fluctuation of successive signals (24-kc), 
and the corresponding autocorrelation graphs (see 
Section 3.5.4). B shows the autocorrelation coefficient 
for the signals in A; D that for the signals plotted in C. 
The ratio of the amplitude of each signal to the average 
amplitude of the signals in the set is plotted. 


The standard deviation is often expressed as a per 
cent of the average x. 






VARIABILITY OF TRANSMISSION LOSS 


63 


It is convenient to measure the fluctuation of 
received signals by their standard deviation, using 
in the calculation a set of N = 50 or more, all received 
within a few minutes. The fluctuation, as measured 
in this way, ranges from 20 to 70 per cent. Values 
smaller than 35 per cent or larger than 50 per cent 
are relatively rare when both projector and receiver 
are near the surface. The average value of a in a large 
number of such measurements of fluctuation, for fre- 
quencies from 10 to 60 kc, is 43 per cent. There is no 
significant dependence of the fluctuation on fre- 
quency in this range. 

Importance of Fluctuation 

For the purpose of plotting graphs like Figures 11 
and 12, the effect of fluctuation has been largely 
eliminated by using the average value of the ampli- 
tude, the average being calculated from a set of 5 
successive pings. For some practical purposes, the 
fluctuation can be ignored and eliminated in much 
the same way. This is true, for example, in most echo- 
sounding operations. There is then sufficient time to 
consider several echoes before arriving at a con- 
clusion. 

In searching operations, however, a given region 
can usually be swept only with one ping, the next 
ping sweeping in another direction. When fluctuation 
makes the echo especially weak, a target may escape 
detection, even though it would be detectable if the 
transmission had been average. 

Use of Medians and Quartiles 

In order to deal with problems such as this, neither 
the average nor the standard deviation is a very 
useful numerical measure. Statisticians have de- 
veloped several other concepts for such purposes : 

The median of a set of numbers x n is a number such 
that 50 per cent of the x n are greater than it, 50 per 
cent less. 

The upper quartile is a number such that 25 per 
cent of the x n are greater than it, 75 per cent less. 

The lower quartile is a number such that 75 per 
cent of the x n are greater than it, 25 per cent less. 

The upper and lower deciles are similarly defined 
in terms of the 10 per cent: 90 per cent division 
of the set. 

In this book, a single measurement of transmission 
loss or anomaly is always the average of the ampli- 
tudes of several transmissions, after conversion to 


db. For some applications it would be preferable to 
use the median of the amplitudes. For other applica- 
tions, when failure to achieve transmission of the 
signal is highly penalized, it would be better to use 
the lower quartile or decile of the amplitudes in mak- 
ing estimates. In still other cases, e.g., when estimat- 
ing the chance of being overheard by a distant enemy, 
the upper quartile or decile should be used. 

The general relation between these various meas- 
ures is shown in Table 4. These values are quoted 
merely as guides and not as accurate values. This is 
especially true of the deciles: values for the upper 
decile as large as 1.95 and as small as 1.42 are not 
uncommon. 


Table 4. Fluctuation in the intensity of transmitted 
signals. 



Ratio to 
average 

Decibels above 
average 

Upper decile 

1.65 

4.4 

Upper quartile 

1.26 

2.0 

Median 

0.97 

-0.2 

Lower quartile 

0.63 

-4.0 

Lower decile 

0.48 

-6.4 


Table 4 emphasizes the great fluctuation in the 
transmission. In order to embrace 80 per cent of the 
signals, a latitude of more than 10 db must be allowed. 
Even if only 50 per cent of the signals are to be in- 
cluded, the limits must be 6 db apart. 

This applies only to one-way transmission. The 
fluctuation in the intensity of echoes is probably 
slightly greater. Thus, on two occasions the fluctua- 
tions of transmission and echo intensity were de- 
termined within one hour of each other. The trans- 
mission fluctuated by 50 and 49 per cent, while the 
corresponding values for echo intensity were 66 and 
69 per cent. A longer series of echo measurements, 
not made simultaneously with transmission studies, 
gave an average fluctuation of 40 per cent. 

354 Autocorrelation 

The Problem 

The standard deviation gives quantitative informa- 
tion concerning the amount of fluctuation; but it is 
easy to see that the rate at which the signal ampli- 
tude changes is also important. A periodicity in the 
fluctuation may suggest a possible cause of the 
fluctuation. 


64 


THE TRANSMISSION OF SOUND IN THE SEA 


Inspection of Figure 53A and C shows that there 
is a difference in the rate at which the amplitude 
changes. In A, a high-amplitude signal is as likely to 
be succeeded by a low one as by another high one; 
whereas in C, a high-amplitude signal is much more 
likely to be succeeded by another one above average 
than by one that is below average. In both cases the 
signals succeeded one another at 3^-sec intervals; 
hence this indicates a different tempo of the ampli- 
tude changes. 

The rate at which the signal amplitude fluctuates 
can be described by calculating a quantity known as 
the autocorrelation coefficient. 

Definition 

As before, let x„ — x be the deviation of the nth 
signal from the average. The calculation of the auto- 
correlation coefficient is similar to that of variance; 
however, instead of squaring the deviation, one com- 
putes the product of the deviation of one item with 
the deviation of another, keeping the separation 
between the items of a pair constant through the 
series. In mathematical symbols, 

Pm = — r (x 1 -x) (xi+ m -x) + O2 —x) (X2 +m ~X) + 

aL 

• • • + (x n -X) ( Xn+m — 2)J, (29) 

where m may equal 1, 2, 3 • • •, but has a fixed value 
throughout a summation. 

It is seen that when m = 0, equation (29) reduces 
to equation (27), hence p 0 = y is the variance. When 
m is different from zero, p m is called the mean dis- 
placed product or the autocorrelation function. It is 
more convenient to use when expressed as a ratio to 
the variance; this ratio is called the autocorrelation 
coefficient. It is often stated as a per cent. The number 
m is the correlation interval. 

It can be shown that the autocorrelation coefficient 
cannot be greater than 100 per cent. It is 100 per 
cent if m = 0 by definition; moreover, by comparing 
equations (27) and (29) it is evident that it is 100 
per cent if, for all values of n, x n + m = x n . Thus, if 
p 2 = 100 per cent, x n and x n + 2 must be equal for all n; 
this means that the fluctuation is periodic, with a 
period of 2. 

The autocorrelation coefficient can never be less 
than — 100 per cent. In that case all the pairs of de- 


viations are equal, but opposite in sign. In both these 
extreme instances the fluctuation is periodic. 

In general, the autocorrelation coefficient will be 
less than 100 per cent for all values of m (except 
m = 0) . If it is always zero, the fluctuation is perfectly 
random. A graph of p m gives information about the 
departures from periodicity on the one hand, and 
about the departures from perfect randomness on 
the other. 

Illustration 

Examples of graphs of autocorrelation coefficients 
are shown in Figure 53B and D. These graphs cor- 
respond respectively to the graphs of the amplitude 
deviations of Figure 53A and C, and illustrate the 
foregoing remarks. In Figure 53B the values of p m 
are rarely greater than 20 per cent; this indicates 
that the fluctuation shown in A is nearly random. 
In Figure 53 D the coefficient remains above 50 per 
cent for 13^ sec and drops to — 50 per cent at 8 sec. 
This means that a high signal is followed by high 
signals for a period of V/i sec, but after 8 sec it is 
followed by unusually low signals. There is thus a 
trace of a 16-sec period in this set of data. In Figure 
53A one can see smaller traces of 5-sec and 8-sec 
periods. 

3.5.5 Cause of Fluctuation 

A number of causes of fluctuation have been sug- 
gested and considered. It appears that no one of 
them is capable of producing all of the known effects. 18 
Four possible causes may be listed : 

1. Roll and pitch of the projector. 

2. Interference between direct sound and surface 
echo. 

3. Interference between sound traveling via many 
different paths. 

4. Focusing and defocusing due to action of local 
thermal inhomogeneities as lenses. 

Roll and Pitch of the Projector 

If cause 1 were dominant, it would be expected 
that the fluctuations would keep step with the mo- 
tion of the ship and that fluctuations at different 
ranges would also keep step. This has not been fully 
investigated, particularly as the motion of both 
transmitting and receiving ships must be considered. 


VARIABILITY OF TRANSMISSION LOSS 


65 


While this cause is apparently not dominant, it may 
explain the traces ol long periodic changes indicated 
by Figure 53 C and D. 

As the range is increased, the fluctuation becomes 
more rapid at the range where the effects of reverbera- 
tion (the “tail”) become prominent (see Figure 52B). 
At all ranges the correlation between signals spaced 
more than 1.5 sec apart is usually less than 0.5. 

If the roll and pitch of the gear were the dominant 
cause of fluctuation, one would expect sound of sonic 
frequencies also to show the effect. Figure 54 shows 
the autocorrelation graph of 5-kc signals at long 


TIME INTERVAL, SECONDS 



Figure 54. Autocorrelation of sonic (5-kc) signals 
at long range. The fluctuation is seen to be practically 
random. 


range. This figure suggests that for sonic frequencies 
the fluctuation is practically random, but this con- 
clusion is based on very little data. 

Attempts to determine the nature of fluctuation 
have included experiments in which the signals were 
received simultaneously on two hydrophones at dif- 
ferent depths, and on two hydrophones at the same 
depth but horizontally separated from 5 to 15 ft. The 
correlation between such signals becomes less with 
increasing range and with greater separation of the 
hydrophones. For ranges greater than about 500 yd 
and when the hydrophones are at different depths, 
the coefficient is practically always less than 50 per 
cent. The significance of these results is not clear. 

Interference Between Direct Sound and 
Surface Echo 

If cause 2 were dominant, the fluctuation would be 
sharply limited, the upper limit being 1 + /x times 
the average, the lower 1 — /x, where /x is the surface- 
reflection coefficient. Since /x is necessarily less than 
unity, the maximum amplitude would be less than 
twice the average. On some occasions, nearly 10 per 


cent of the observed amplitudes are more than twice 
the average. The fluctuations almost never are sharply 
limited, but show some very large and very small 
values at long intervals. Thus cause 2 cannot be the 
only one acting. 

However, experiments performed with both pro- 
jector and hydrophone at a depth of more than 500 
ft (Section 3.2.8) make it possible to separate the 
direct and surface-reflected sound. At short ranges 
(less than 500 yd), the fluctuation of the direct sound 
was only 20 per cent, while that of the surface-re- 
flected sound was 50 per cent. This suggests that, 
although the simple theory of interference is not 
applicable, surface reflection may be an important 
factor in fluctuation. 

At longer ranges, with deep projector and hydro- 
phone, the fluctuation of both direct and surface- 
reflected sound is about 50 per cent. 

It may also be noted that, in experiments with 
explosive sound, direct and surface-reflected sound 
can be separated (Section 3.1.2). In some of these 
experiments the fluctuation of direct sound was less 
than 10 per cent. 

Other Causes — Summary 

Causes 3 and 4 are not open to these objections, 
but as yet thermal measurements have shown no 
reason to expect local variations in the velocity of 
sound which are large enough to account for the 
observations. 

Probably all these causes act together in propor- 
tions that change from day to day. 

If causes 2 or 3 were dominant, it would be ex- 
pected that sounds of different frequency, transmitted 
simultaneously, would be affected differently. At a 
time when the transmission of one frequency is poor, 
that for another would be good. Such simultaneous 
transmission of many frequencies can be approxi- 
mated by transmitting “chirp” signals, in which the 
frequency changes during the transmission. An ex- 
periment with chirps in which the frequency changed 
from 23.5 to 24.5 kc showed about 15 per cent less 
fluctuation than did single-frequency pings on the 
same day. This result might be accidental, and 
further study is needed. 

Signals of 16 kc and 24 kc were emitted simul- 
taneously by the same projector and received by the 
same hydrophone, as well as signals of 24 and 56 kc. 
The correlation between such pairs of signals aver- 
aged 30 per cent. Sets of signals of the same fre- 


66 


THE TRANSMISSION OF SOUND TN THE SEA 


quency have a standard deviation of about 70 per 
cent. This suggests that a significant portion of the 
fluctuation at each frequency is due to a common 
cause. 

3 5 6 Variation of Transmission 

Mention was made in Section 3.5.1 of slow changes 
in the transmission loss, which become apparent 
when the average amplitude of a number of pings at 
one time is compared with that of another set re- 
ceived at a later time. These slow changes were 
designated variation. 

Treatment of Data 

In assembling data for the study of the long- 
period changes, the following procedure was carried 
out. 

The oscillograms used were those obtained during 
a single experiment in which the receiving vessel 
drifted and the transmitting vessel opened or closed 
the range (see Section 3.2). The amplitude of suc- 
cessive received signals were determined ; sets of five 
nonsuccessive signals were averaged to eliminate 
some of the fluctuation. Nonsuccessive pings were 
chosen in order to avoid the possible effects of correla- 
tion. These averages were plotted as a function of 
range. After a large number of such graphs had been 
accumulated, they were sorted into more or less 
homogeneous sets, according to the depth of the 0.3°F 
decrease, D 2 . From each graph, the value of the 
transmission anomaly was read at certain ranges, and 
plotted on a graph like the one shown in Figure 55. 
This figure is the set of data for values of D 2 lying 
between 10 and 20 ft. The hydrophone depth for 
most of the points was 16 ft and for all of them less 
than 40 ft. 

Despite the relative homogeneity of the condi- 
tions under which the measurements were made, 
the points scatter very widely. This is the phenomenon 
which has been called variation. The most convenient 
method of discussing the variation is by using medians 
and quartiles, defined above. In Figure 55, the median 
values at various ranges are connected by the solid 
curve, the quartile values by dotted curves. The 
median and quartile values are also given in Table 5, 
together with the average deviation of the quartiles 
from the respective medians; this quantity is called 
the quartile deviation. It is indicated on the graph by 
half the vertical spread between the dotted curves. 


Table 5. Variation of the transmission anomaly at 
various ranges.* 


Range 

(yd) 

Lower 

quartile 

(db) 

Median 

(db) 

Upper 

quartile 

(db) 

Quartile 

deviation 

(db) 

250 

0 

2 

4 

2 

500 

2 

5 

8 

3 

1,000 

12 

12 

26 

7 

1,500 

26 

31 

37 

5.5 

2,000 

31 

38 

41 

5 

2,500 

30 

39 

46 

8 

3,000 

29 

38 

48 

9.5 

4,000 

27 

34 

48 

10.5 

5,000 

24 

28 

47 

11.5 


*Data from Figure 55. 


Similar results are obtained under other conditions. 
It is seen from Figure 55 and Table 5 that there is a 
marked increase in the scatter as the range increases. 

The Causes of the Variation 

The possible causes of variation are of two kinds: 
those which originate in the apparatus, and those 
which originate in the sea. There are many possibili- 
ties of the first kind, but most of them have been elim- 
inated by the experimenters and need not be discussed 
here. The outstanding sources of error that remain are: 

1. Uncertainty in the zero of the anomaly scale. 

2. Uncertainty in the orientation of the hydro- 
phone. 

3. Residual effects of fluctuation, not eliminated 
by averaging five pings. 

All of these sources of error might cause variation ; 
but none will explain the increase in the quartile 
deviation with increasing range. This is obvious in 
causes 1 and 2. In the case of fluctuation (cause 3), 
it follows from the fact that the percentage fluctua- 
tion is independent of range. 

Concerning the first cause— uncertainty in the 
zero of the anomaly scale — no attempt has been 
made to measure the received sound pressure in 
dynes per square centimeter in the work with 
supersonic sound. Only changes in sound level are 
measured. These relative levels are plotted with 
reference to the level of the sound received at 1 yd 
from the projector. In practice, the level at 1 yd is 
not actually measured, but is estimated by extra- 
polating from a measurement taken at 100 or 200 yd, 
assuming that H = 20 log r from 1 yd to this distance. 
Consequently, all transmission-loss measurements 
may be too high or too low by the amount of error 


VARIABILITY OF TRANSMISSION LOSS 


67 


RANGE, YD 


0 1000 2000 3000 4000 5000 6000 


-10 

0 

10 

§ 20 

-1 

< 

2 

° 30 

< 

40 

50 

60 

• 

. . 

•• •• 

•••••• •• 






•••• 

• T\\ 

• 





\ \ \ 

T-\\\ 

\ \ \ 

: \V 

> • • 

I • • 

> • 

» • 

r • • 

>•••• 

• 

• 

• 

• 


: 

> 

\: 

•N 

£\ • 

► \ V • • 

•*\ '» 
v \ • • •• 

v \m»*«** v 

• • 

• 

• 

• < 

• • < 

• < 

• • 4 

• < 

: 

> • 

• • 

j 

• \ • 

• • 

!•“ • < 
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• • i 

• • < 

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t • ' 

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: 

4 

• 

• 

• • 

»• • • i 

• 4 

• •• 4 

••• 4 

x w • • • 

• 

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>• 4 

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i • 

• EXPERIMENTAL 

MEDIAN VALUES 

QUARTILE VALUES 


• 4 

• 4 

• 

• 

« 

> • < 

• 

• 

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• 

• 


Figure 55. Variation of 24-kc sound. Each point represents the average of five nonsuccessive signals received during 
a single experiment; the median and quartile values at the various selected ranges are connected by lines. Hydrophone 
depth for most points = 16 ft; for all the points, < 40 ft. 10 ft <D 2 < 20 ft. 


involved in this extrapolation. The correction of this 
error is not easy, although later measurements are 
less subject to it than the earlier ones. The error may 
change from day to day and thus contribute to the 
variation. If this were the only cause of the variation, 
however, the difference between the upper and lower 
quartiles would be the same at all ranges. 


It follows that the total effect of the three causes 
listed cannot be greater than the smallest observed 
variation. From Table 4 this is seen to be ±2 db for 
the difference between quartiles and median at 
250 yd. At 3,000 yd this difference is of the order + 9 
db. Thus it may be concluded that some other cause 
is operative. 



Chapter 4 

THE OCEANOGRAPHY OF SOUND CONDITIONS 


4.1 INTRODUCTION 

I t has been made abundantly evident in Chapters 
2 and 3 that the transmission of sound in the sea 
is decidedly influenced by the temperature conditions 
in the upper layers; in particular, temperature dif- 
ferences of a fraction of 1°F, occurring in the upper 
40 or 50 ft of the ocean, can strongly influence sound 
transmission. 

These surface gradients are extremely variable: 
they change from season to season, from day to day, 
even from hour to hour, and from place to place. In 
this respect the ocean is very similar to the atmos- 
phere, and thus there is a close analogy between 
oceanography, on the one hand, and meteorology and 
climatology on the other. One may speak of the 
subsurface weather and of its seasonal and diurnal 
changes, and of the subsurface climate, the annual 
and seasonal averages of the components of the 
weather. The analogy between oceanography and 
meteorology holds true further in that one of the 
practical objectives of the oceanography of under- 
water sound is the forecasting of subsurface weather. 

The study of subsurface weather was neglected 
until its importance for underwater acoustics was 
recognized. The results of this study are discussed 
fully in another volume of this series. 1 In the present 
chapter only a brief summary of the acoustically 
significant results can be given. 

The outstanding characteristic of weather, whether 
in the air or under the sea, is its changeability. These 
changes are the outcome of a complex set of processes, 
which are continuously in action. Sometimes one of 
these processes may dominate all others; more often, 
several will exert appreciable influences on the 
resultant. 

There are at least ten or a dozen such processes 
which cause the temperature gradients in the upper 
layers of the ocean to change. They can conveniently 
be grouped into four general processes, and these will 
be discussed first. Their effects in the form of daily, 
seasonal, and geographic changes of the temperature 
gradients will then be described. Finally, the more 
detailed analysis of the general processes will be 
given. 


4 2 THE GENERAL PROCESSES AND THEIR 
INTERACTION 

4.2.i General Survey 

The surface layers of the ocean are subjected to 
heating, cooling, and mixing; moreover, they may 
flow at a speed different from that of the underlying 
water. These are the four general processes just 
mentioned. All four processes are closely interrelated 
but each has its own characteristic effect on the 
temperature gradients that are revealed by bathy- 
thermograms. Each of them is caused by a variety of 
factors; all four, however, are affected by the condi- 
tion of the atmosphere at the ocean surface. The 
immediate effect of each is to alter the dynamic state 
of the surface layers. 


Table 1 . Outline of processes influencing temperature 
changes. 


General 

process 

Cause 

Dynamic 

effect 

1. Heating 

Sunshine, 

Warm moist air 

Stability of 
surface layer 

2. Cooling 

Evaporation, 

Radiation, 

Cold dry wind 

Instability 
of surface 
layer 

3. Mixing 

Wind and waves, 

Instability, 

Turbulence 

Neutral stability 
of surface layer 

4. Flowing 

Wind and waves, 
Internal waves, 
Currents 

Variable; 
turbulence if 
strong 


Table 1 presents an outline of the general processes, 
their causes and dynamic effects. A characteristic 
complication is illustrated by processes 2 and 3: 
cooling has the effect of making the surface layer 
unstable, and instability in turn is a cause of mixing. 
In the same way, strong currents may cause tur- 
bulence, which again results in mixing. There 
are other chains of cause and effect linking all the 
processes. 


68 


THE GENERAL PROCESSES AND THEIR INTERACTION 


69 


4 . 2.2 Stability 

Stratification of the Ocean — an Equilibrium 
Condition 

Bathythermograms show that the ocean is more or 
less stratified. Two points separated by several 
hundred yards but at the same depth beneath the 
surface will have practically the same temperature. 
If the ocean were in equilibrium, this stratification 
would be complete: the warm, lighter water being at 
the surface, the lower strata consisting of cooler, 
heavier water, and the boundaries between strata 
being horizontal surfaces. The equilibrium is dis- 
turbed by three of the four general processes. The 
observed stratification is thus the result of other 
processes tending to bring the ocean to equili- 
brium. 

Density a Function of Temperature and 
Salinity 

It is a general hydrodynamic principle that when a 
mass of fluid is in stable equilibrium under the force 
of gravity its density must everywhere increase in the 
downward direction and be constant in every hori- 
zontal plane. A commonplace illustration of this 

TEMPERATURE, F 



Figure 1 . Variation of the density of sea water with 
temperature and salinity. 


principle is furnished by a bottle containing oil and 
water. 

The density of sea water is primarily determined 
by its temperature and salinity, as shown in Figure 1. 


The changes due to temperature are the largest, 
just as in the case of the velocity of sound (see Figure 
1 of Chapter 2) . However, salinity has a proportion- 
ately greater effect on the density of sea water than 
on the velocity of sound. 

In the open ocean, where the salinity is practically 
constant, the lighter water will thus always be the 
warmer water, and it is to be expected that the 
temperature will either remain constant or decrease 
with increasing depth. With very rare exceptions, 
this is found to be the case. Near the shore, salinity 
differences may sometimes dominate the density 
distribution so that a layer of cold dilute water may 
overlie warmer water of high salinity. 


Thermal Structure and Stability 

The concept of stability is a convenient one to 
apply. Stability depends on the rate at which density 
increases with depth. If the temperature in a layer 
decreases rapidly with depth, as in the thermocline, 
the layer has a high stability, for in this case the 
density increases rapidly. On the other hand, a layer 
in which the density decreases with depth is unstable 
and will exist only transiently. Mixing processes are 
retarded by high stability; thus wind of a given 
strength may easily mix a surface layer in which the 
temperature gradient is small and the stability, 
therefore, low. The same wind may have little mixing 
effect if the temperature gradients near the surface 
are large. The development of a sharp thermocline 
tends to retard mixing to greater depths. 

A completely mixed isothermal layer has indiffer- 
ent stability. Cooling at the surface increases the 
density of the surface layer. So also does evaporation, 
because of the cooling and the increase in salinity 
that accompany it. Hence these processes tend to 
make the density of the surface water greater than 
that of the wq,ter immediately below it and to pro- 
duce a condition of instability. This unstable density 
distribution near the surface results in convective 
mixing. 

The stability can be estimated from a bathy thermo- 
gram if it is assumed that salinity gradients are 
negligible. Density decreases with increasing tempera- 
ture (see Figure 1) and for most practical purposes 
the isotherms on the bathythermogram grid can be 
interpreted as lines of equal density. The slope of 
the temperature trace is therefore a measure of the 


70 


THE OCEANOGRAPHY OF SOUND CONDITIONS 



Figure 2. Experiments with density layers. (A) Both layers at rest. (B) Dye streaks showing particles transported 
by currents. (C) Surface waves do not disturb the boundary of the lower layer. (D) Internal waves do not disturb the 
surface. (E) and (F) Mixing in the upper layers due to long-continued surface waves. 




THE GENERAL PROCESSES AND THEIR INTERACTION 


71 


rate of change of density with depth; that is, of 
stability. With this in mind, the bathythermograph 
traces can be interpreted in terms of the four major 
processes. 

423 Laboratory Experiments on 
Stratification 

The high stability of negative thermal gradients 
is due to the fact that there is little exchange of heat 
between neighboring layers unless they are mixed by 
some stirring action. This is readily shown by labora- 
tory experiments. If a tank is partly filled with warm 
water, and water of room temperature is then run in 
through a hose lying on the bottom, the warm water 
will float on the colder. Thermometers placed in the 
two layers will show that the cooler water is not 
heated by the overlying warm water. The latter will 
cool, as described below. 

Photographs of experiments with density layers 
are shown in Figure 2. The layers were produced in a 
tank having transparent walls, and the upper, lighter 
layer was colored to facilitate observations. Figure 
2 A shows both layers at rest. The dark vertical 
streaks were obtained by dropping bits of dyestuff 
into the water. Figure 2B shows how these particles 
are transported by currents set up in the top layer. 
The boundary of the lower layer persists undisturbed 
by surface waves, as seen in Figure 2C; conversely, 
Figure 2D shows an internal wave causing changes 
in the level of the boundary of the two layers without 
showing on the surface. The internal waves were 
created mechanically and are not caused by the 
surface disturbance. Figures 2E and 2F show the 
effect of long-continued surface waves on mixing in 
the upper layer. 

This stability of layers when the temperature 
gradients are negative is in marked contrast to the 
instability of positive temperature gradients. Re- 
turning to the experiment of warm and cold layers of 
water in a tank, the surface of the warm layer may 
be cooled by blowing a gentle stream of cold air 
over it. The cooling of the layer at the immediate 
surface causes it to become heavier than the water 
beneath it. Consequently it sinks and in so doing 
mixes with and cools the underlying water. Two 
thermometers at different depths in the warm 
layer will show that cooling proceeds nearly simul- 
taneously at all depths, without the development 
of large positive temperature gradients. The mix- 


ing which accompanies cooling is called convective 
overturn. 

4 2 4 Effects of the General Processes on 
Temperature Structure 

Heating 

The progressive or intermittent effects of the four 
processes — heating, cooling, mixing, and flowing — 
lead to the complicated and variable conditions 
illustrated in Figure 4. The manner in which any one 
of these processes will operate individually to change 
the bathy thermogram is shown in Figure 3. The 
change in temperature distribution produced by 
solar heating is illustrated by curves 1, 2, and 3 in 
Figure 3A. Initial conditions, indicated by curve 1, 
are assumed to be isothermal. The absorption of heat 
together with some mixing results in curve 2 and 
finally curve 3. Negative gradients extending from 
the surface downward are characteristic of recent 
heating. The negative gradients, and consequently 
the stability, will be greater the smaller the amount 
of mixing that occurs during the heating. Under these 
conditions, wind is the principal cause of mixing. 

Cooling 

The cooling that takes place during the night and 
during the winter is essentially a reversal of the 
process of heating. Starting with curve 1 in Figure 
3B, assumed to be the same as curve 3 in the preced- 
ing diagram, surface cooling with its accompanying 
convective overturn produces curve 2 and ultimately 
curve 3 and if continued for a long enough period 
would finally produce completely isothermal water. 
Although the cooling takes place at the surface, 
measurable positive gradients do not develop be- 
cause of the mixing involved in the convective over- 
turn . Winds hasten this mixing process, but convective 
overturn takes place even in very calm weather. 
Theoretically, the upward transfer of heat must be 
associated with slight positive gradients, but these 
are so small that they usually escape detection. 

Mixing 

The result of vigorous mixing by the wind, when 
there is no gain or loss of heat by the surface layer, 
is illustrated in Figure 3C. It will be noted that in 


72 


THE OCEANOGRAPHY OF SOUND CONDITIONS 



SURFACE LAYER 
HEATED 



COOLED 



SURFACE LAYER 
MIXED 



SURFACE LAYER 
ALTERED BY CURRENTS 


Figure 3. Manner in which the general processes 
working individually change the bathythermogram. 
(A) Development of negative gradient by heating of 
surface layer. (B) Development of isothermal surface 
layer by cooling. (C) Development of isothermal sur- 
face layer by mixing. (D) Effect of currents: 1, 2, 3, 
show development of an isothermal layer; (1), (2), 
(3), of a negative gradient. 


this example surface isothermal layers develop just 
as they did in Figure 3B, and the surface temperature 
decreases, but the temperature distribution im- 
mediately below the mixed layer is of a different 
character. The wind mixes warm water with cooler 
water beneath it, increasing the temperature at 
intermediate depths, and thus produces a very sharp 
thermocline instead of retaining the initial gradients 
(as was the case when cooling was the primary cause 
of the mixing). Curve 1 in Figure 3C is the same as 
curve 1 in Figure 3B, but the result of wind mixing 
without cooling produces distributions quite dif- 
ferent from those resulting from cooling alone. 
Obviously, conditions intermediate between those of 
Figures 3B and 3C will often develop, since cooling 
and wind mixing can occur simultaneously. 


Flowing 

The effect of addition or removal of water by cur- 
rents is illustrated in Figure 3D. The transfer of 
water can be produced by various causes, among 
them winds. If warm surface water is carried over 
the top of cooler water, a progressive change in 
temperature distribution may occur, as illustrated by 
curves 1 , 2, and 3. If warm surface waters are removed, 
the reverse sequence may develop, that is, the one 
indicated by numbers (1), (2), and (3). It will be 


noted that the gradients remain unchanged and are 
merely lowered or raised. Internal waves, similar to 
those illustrated by Figure 12, which periodically 
raise and lower the thermocline, can cause similar 
effects in a very short time. These waves may be 
single or have a well-defined periodic character and 
are accompanied by single or periodic surges of current. 


Temperature Distribution 

The processes described above all involve passage 
of time, that is, continued heating, cooling, wind 
mixing, or flowing produce progressive changes in the 
temperature distribution. In the sea the temperature 
distribution in a given locality is the result of inter- 
play of all four processes. For a limited time, say, 
during one afternoon, one of them may dominate, so 
that it is possible to say that the temperature condi- 
tions near the surface are the result of heating, or of 
cooling, or of wind mixing, or of currents. The com- 
plicated distributions illustrated in Figure 4 are 
usually the result of intermittent action of the four 
general processes. 


Thermal Structure at Great Depths 

It should be noted that all these processes except 
the flowing originate at the sea surface and that their 
effects are propagated to greater depths by convective 
overturn or mixing or both. These effects are rarely 
noticeable at depths greater than 600 to 700 ft. Below 
this level, stable stratification exists at all times, and 
the only changes are due to slow seasonal currents. 
This deep region is therefore characterized by the 
so-called permanent thermocline or negative tempera- 
ture gradient, discussed in Section 2.2. 2 

The density of sea water increases with decreasing 
temperature down to the freezing point (about 
28.5°F), which sets a lower limit for the temperature 
in the sea. Below 6,000 ft the temperatures every- 
where are less than about 37.5°F and decrease with 
depth; they also decrease towards the south, where 
the coldest water is formed. 4a The circulation of the 
deep, cold water is exceedingly slow, probably of the 
order of 1 ft/minute. For all practical purposes the 
conditions in the deep sea do not change with time; 
they do, however, vary slightly from one region to 
another. In any one locality below about 3,000 ft the 
temperature decreases slowly and the salinity is 
either constant or increases slightly with depth. The 
effects on the velocity of sound of the oceanographic 


DEPTH IN FEET DEPTH IN FEET DEPTH IN FEET 


THE GENERAL PROCESSES AND THEIR INTERACTION 


73 


DEGREES FAHRENHEIT 


DEGREES FAHRENHEIT 



DEGREES FAHRENHEIT 


DEGREES FAHRENHEIT 



MAY 

DEGREES FAHRENHEIT 




JULY 


DEGREES FAHRENHEIT 



SEPTEMBER 


NOVEMBER 


Figure 4. Annual cycle of ocean temperature gradients (40° N 170° W). 



74 


THE OCEANOGRAPHY OF SOUND CONDITIONS 


JAN FEB MAR APR MAY JUN JUL AUG SEPT OCT NOV DEC 



Figure 5. Annual cycle of temperature in the ocean. The curves show the depth at which the indicated temperature 
occurs at various times of the year. 


conditions at great depths have been mentioned (see 
Sections 2.2 and 2.3.3). Transmission of sound at 
great depths was discussed in Chapter 3. 

4 . 2.5 The Annual Cycle 

In middle and higher latitudes, there is a marked 
annual cycle in temperature conditions. The cycle 
can be observed in Figure 4, which is based on 
bathythermograms taken in the open ocean, in 
latitude 40° N in the North Pacific. It is convenient 
first to consider conditions in March : the isothermal 
layer is more than 450 ft thick, and was produced 
by cooling and by mixing induced by winter’s storms. 
In May some heating of the surface layers has oc- 
curred, and mixing by winds has produced an upper 
isothermal layer of a slightly higher temperature 
than the original ; thus, there is a small thermocline 
at a depth of about 150 ft. The negative gradient at 
the surface probably represents heating during the 
day and will either be obliterated by wind mixing or 
disappear during the night because of cooling and 
convective overturn. Progressive heating continues 
through the summer months so that the temperature 
near the surface increases, as shown by the July and 
September bathythermograms ; but wind maintains a 
mixed layer with a rather sharp thermocline which 
increases in depth as the season progresses. In the 
fall, cooling once more exceeds heating; the surface 
isothermal layer becomes cooler and, with the added 


effect of strong winds, the thermocline goes deeper, 
until in January it is below 400 ft. Cooling and mix- 
ing continue until about March. 

Figure 5 is another way of summarizing the annual 
cycle. The curves are isotherms that show the depth 
at which a given temperature occurs, as a function 
of time throughout the year. The gradual variation 
of thickness of the isothermal surface layer is very 
apparent. The close spacing of the curves noticeable 
from June to November indicate steep gradients. 
The discussion of Figure 4 applies to this figure with 
minor changes, e.g., the negative gradient caused by 
surface heating does not become marked until early 
June. These differences are probably within the 
normal variability of the seasons. 

In general, the systematic seasonal changes are 
subject to modification by local weather conditions. 
The mixing of the surface layer by wind is especially 
important in this connection. In Figure 6, the average 
temperature decrease in the top 30 ft is plotted for 
each season as a function of wind force. It is seen 
that high winds can practically obliterate the 
seasonal trend. 

426 The Diurnal Cycle 

The diurnal cycle in temperature conditions is 
in many ways a miniature replica of the annual 
cycle, but it must be remembered that during the 
spring and summer progressive heating will occur 


THE GENERAL PROCESSES AND THEIR INTERACTION 


WIND FORCE, BEAUFORT 



Figure 6. Effect of wind on average temperature 
gradient in surface layer during various seasons. 


and that during the fall and winter there will be 
progressive cooling and mixing. Consequently, the 
daily cycle will sometimes be practically obliterated 
by the progress of the seasonal changes. 

Four selected examples of diurnal changes are 
given in Figure 7. The data are from the open ocean 
and are based on bathy thermograms taken over 
periods of from 23 to 48 hr during the summer 
months. Each set has been adjusted so that the 
temperature at a depth of 50 ft is used as the refer- 
ence. The heating is indicated by shading. 

Series A was taken during a day when winds aver- 
aged Force 3 at all times. Although heat was added to 
the water, the stirring action of the wind caused a 
mixed layer to persist near the surface throughout 
the day. The layer is so shallow, however, that poor 
sonar conditions would prevail during the afternoon. 
During the night, cooling and mixing resulted in 
isothermal conditions to a depth of 50 ft. 

Series B is an example of heating on a day with 
light winds when negative gradients extended to the 
surface during the late morning and afternoon. 
Beginning at 1800, a mixed layer was present and 
cooling continued during the night. It is of interest 
that an observation at 0600 next morning showed 
a small positive gradient which had disappeared 
at 0800. 

Series C covers a period of approximately 48 hours 
with variable winds. No progressive heating is 
noticeable and there is a return to isothermal con- 
dition each night. 

Series D is an example of heating when a negative 
gradient existed early in the morning. The shallow 
isothermal surface layer had practically disappeared 
at noon; the gradient became progressively more 
pronounced during the day, and persisted during the 
following night. 



0600 0800 1000 1200 1400 1600 1800 0600 0800 




! 

n / ' / : 


5 





i / / i J 

[ / i / i f 







z_JLZd 












WIND FORCE 2 48°N-I49°W SEPTEMBER 9, 1943 



WIND FORCE I TO 4 4O°N-l50°W JULY 25 27, 1944 


D 


! I 1 

; it / 

' ; 

• — — : ^ — - — r 


rt t 

i 7 T 

i / i / 

\/ 

j- ■ yr 


i/U 

! / ! / / !/ i / ' / 

L I 1 If 1 / / 

7 / i v . . i / . / / - 


WIND FORCE 2 AND 3 4g , N-l47‘W JULY 24,25,1944 


Figure 7. Diurnal cycle of ocean temperature gradi- 
ents. (A) Persistent mixed surface layer. (B) Typical 
diurnal cycle with light winds. Note slight positive 
gradient at 0600. (C) Variable winds with changeable 
pattern. No progressive heating. (D) Persistent nega- 
tive gradients. 

As in the case of the annual cycle, high winds can 
obliterate the daily cycle in the upper 30 ft. This is 
shown by Figure 8. 


The Afternoon Effect 

In general, strong, negative surface gradients are 
most common in the afternoon. Because of its im- 
portance, this has been called the afternoon effect. 
The gradients reach a maximum at about 1600, and 
have a minimum in the morning, about 0600. They 
are more common during the summer months than 
during the winter. This is easily explained, since the 
solar radiation is greatest in the summer. 

This simple explanation is essentially correct, but 
fails utterly to provide an explanation of the geo- 
graphical distribution of afternoon effect. Instead of 
being most frequent at the equator, where solar 


76 


THE OCEANOGRAPHY OF SOUND CONDITIONS 


WIND FORCE, BEAUFORT 



Figure 8. Effect of wind on average temperature 
gradient in surface layer at various times of day. 


radiation is greatest, the afternoon effect is actually 
less frequent there than in high latitudes. Solar 
radiation is undoubtedly the primary cause of the 
negative surface gradients, but the magnitude of 
its effect is modified by the other three factors, es- 
pecially wind mixing and evaporation. (See 
below.) 

While afternoon effect in the open ocean is most 
frequent in high latitudes, this is not necessarily true 
inshore. The waters off Southern California, for 
example, are notorious for the prevalence of after- 
noon effect. 


4 3 DETAILED ANALYSIS OF THE 
FOUR PROCESSES 

The preceding sections have indicated the general 
types of temperature distribution encountered in the 
sea and the four major processes which affect the 
temperature conditions. Their causes will now be dis- 
cussed. 

4.3.1 Heating and Cooling 

The temperature structure of the ocean is deter- 
mined primarily by its heat content, which is a con- 
stantly varying quantity. There is a continuous 
exchange of heat at the surface of the ocean. The 
ocean receives heat by absorption of the sun’s radiation 
and by the condensation of water vapor in the air, 
when the water is colder than the air. The ocean 
loses heat by radiation to the sky, by evaporation 
of water vapor when the water is warmer than the 
air, and possibly by conduction. Of the received heat, 
by far the largest quantity is due to incoming solar 


radiation. Over the ocean as a whole it is balanced by 
the cooling resulting from reradiation and evapora- 
tion. The effects of other processes are comparatively 
negligible. 

Incoming Radiation 

The incoming radiation includes the invisible 
infrared and ultraviolet as well as the visible light. 
Since it is received from the sun and sky it obviously 
varies with latitude, time of year, time of day, and 
the atmospheric conditions, particularly the cloud 
cover. The total energy received during the year 
decreases with increasing latitude, and in the lower 
latitudes of the tropical regions the seasonal variation 
is small, but with increasing latitude the difference 
between the amounts received during summer and 
winter becomes very great. The effect of clouds is 
very pronounced : a heavy cover of cloud may reduce 
the incoming radiation to less than 25 per cent of 
that received on a clear day. 

Direct heating of the water by the sun is limited to 
relatively shallow depths (Figure 9). Only about 3 
per cent of the radiation penetrates below 300 ft and 
over 50 per cent (all of the infrared) is absorbed in 
the first few inches. If there were no compensating 
heat losses and no mixing, fantastically high-surface 
temperatures and extremely sharp negative gradients 
just below the surface would occur. The penetration 
of light varies somewhat from place to place depend- 
ing upon the amount of suspended debris and organic 
pigments in the water. The foregoing discussion ap- 
plies to the open ocean; near shore and in areas of 
vigorous plant growth the water is practically opaque 
to all wavelengths. 

In addition to the direct solar radiation, the sea 
surface also receives some infrared from the air. 
While this is an appreciable source of heat, it is cus- 
tomary to subtract it from the corresponding infra- 
red radiation emitted by the sea surface. 

Effective Back Radiation 

Effective back radiation is the term used for the 
excess of infrared emitted by the sea surface over 
that received from the air. 3a This balances somewhat 
less than one-half of the incoming solar radiation, 
on the average. It decreases with increasing water 
temperature and with increasing humidity and cloud 
cover. With heavy, low-lying clouds present, the 
effective back radiation drops to less than 25 per cent 


DETAILED ANALYSIS OF THE FOUR PROCESSES 



Figure 9. Spectrum of radiant energy at various depths in the ocean. Inset: percentage of incident radiation reaching 
various depths. (From: The Oceans , Sverdrup, Johnson, Fleming, Prentice Hall, 1942.) 


of that on a clear day, largely because the clouds are 
themselves sources of infrared and radiate heat into 
the ocean on their own account. It was mentioned 
above that clouds prevented direct solar radiation 
from reaching the sea surface. Heat losses from back 
radiation occur in the uppermost fraction of an inch 
of the water and are transmitted to greater depths 
by convective overturn and wind mixing. 

Evaporation 

Evaporation depends primarily upon the tempera- 
tures of the water and the air, the humidity and the 
wind strength. Evaporation can best be understood 
by considering the process as one of transfer of water 
vapor away from the surface. The greater the water- 
vapor gradient the more rapid the evaporation and 
hence the greater the heat loss. Cold, dry air overlying 
warm water therefore favors rapid evaporation. High 
winds increase evaporation by removing the water 
vapor. 

The relative importance of the heat losses through 
evaporation and back radiation can be seen from the 
average heat budget between 70° S and 70° N. 

Heat Budget of the Ocean 4 
Total heat received =0.221 cal/cm 2 /min 

Evaporation losses =0.118 cal/cm 2 /min 

Effective back radiation = 0.090 cal/cm 2 /min 
Conduction to atmosphere = 0.013 cal/cm 2 /min 
Total heat lost =0.221 cal/cm 2 /min 


4.3.2 Mixing Processes 

Convective Overturn 

Thus far only the cooling effect of evaporation has 
been considered. When surface water cools, its density 
increases and causes convective overturn. Equally 
important is the increase in salinity resulting from 
evaporation; the increased density arising from this 
cause contributes greatly to overturn and the de- 
velopment of isothermal surface layers. Thus, cool- 
ing by evaporation is even less likely to be accom- 
panied by positive temperature gradients than is 
cooling by back radiation. 

Conditions that tend to lessen the salinity of the 
surface layer would, of course, have the opposite 
effect, and would tend to favor the development of 
positive gradients. Such a condition might result 
from precipitation. For the ocean as a whole, how- 
ever, evaporation exceeds precipitation; this is shown 
in Figure 10. It will be noted that regions of excess 
evaporation in low and mid-latitudes correspond to 
regions of relatively high surface salinity and deep 
thermoclines. Just north of the equator and in lati- 
tudes above 40°, where precipitation exceeds evapora- 
tion, the surface salinity is low. 

The deficit in the water content of the ocean that is 
caused by the general excess of evaporation over 
precipitation is made up by runoff from land. Near 
land, and especially near the mouths of rivers, sur- 
face salinities are lower than in the open ocean, 


78 


THE OCEANOGRAPHY OF SOUND CONDITIONS 


NORTH LATITUDE 

50 40 30 20 10 


SOUTH LATITUDE 

10 20 30 40 50 


^ 36.00 
> 

H 35.00 
Z 

< 34j00 

*0 












EVA 

PORA 

\ 

TION 


\ 



























/ 









PRE 

:cipit 

ATIOr 

'J 







SUF 

RFACE 

SAL 

.INITY 








\ 






























Figure 10. Variation of average evaporation, pre- 
cipitation, and salinity with latitude. Shaded areas 
show regions where precipitation exceeds evaporation. 


or at depth. This favors the development of posi- 
tive temperature gradients, since it increases their 
stability. 


Mechanical Mixing 

Mechanical mixing is caused by wind and does not 
necessarily involve any gain or loss of heat; neverthe- 
less it may modify the temperature distribution, as 
has already been seen. The effect of winds depends 
not only upon their strength, but also on their dura- 
tion and on the distance over which they have 
blown. It is quite obvious that the first effect of the 
wind will be confined to the immediate surface, but 
that the turbulence will extend to greater depths 
after the wind has been blowing for some time. 
The original density distribution of the surface 
layer will affect the rate at which the turbulence 
penetrates the layer. A very stable layer will be less 
easily mixed. 

Effect of Rotation of the Earth 

It is a remarkable fact that the daily rotation of 
the earth about its axis also affects the depth to which 
the wind mixing penetrates. A discussion of current 
theories 3b>4 of this effect would lead beyond the 
scope of this book, but all agree that a wind of given 
force will ultimately produce a deeper mixed layer 
in low latitudes than in high. 


WIND FORCE, BEAUFORT 
0 1 2 3 4 5 6 7 



Figure 11. Effect of wind on temperature gradient 

in the surface layer at various latitudes. 

This is probably part of the explanation of the data 
shown in Figure 11, which indicate that strong nega- 
tive gradients are most apt to be formed in high 
latitudes. If negative surface gradients are interpreted 
naively as being the result of solar heating alone, this 
is most unexpected, since heating is greatest at the 
equator. The necessity of considering all four of the 
major processes, together with the detailed mechan- 
isms causing them, is emphasized by this figure. 

433 Transport by Currents 

Drift Currents 

The frictional drag of the wind sets up drift cur- 
rents which flow at less than 3 per cent of the wind 
velocity. These drift currents do not flow with the 
wind, but are deflected 45 degrees to the right in the 
northern hemisphere and 45 degrees to the left in the 
southern hemisphere. This is caused by the earth’s 
rotation and is closely related to its influence on the 
depth of mixing which was just discussed. The same 
sources may be consulted for details. 

Permanent Currents 

The redistribution of density resulting from the 
wind-drift currents in turn maintains the 'permanent 
currents. Under the influence of the steady wind sys- 
tems, such as the trade winds in the lower latitudes 
and the westerlies in higher latitudes, these permanent 
currents form the large-scale current system of the 
oceans. They are thus partly the indirect result of 
geographic differences in the heating and cooling of 
the water and partly the result of wind action. The 
character of the currents is also influenced by the 
configuration of the oceans, but in general there are 



GEOGRAPHICAL VARIATIONS 


79 


clockwise gyrals in the northern hemispheres and 
counterclockwise gyrals in the southern hemisphere. 
Smaller currents related to land topography and local 
climate exists near the continents. A countercurrent 
flows eastward between the two westward-flowing 
equatorial currents. 

The permanent currents have several effects on the 
temperature conditions. Currents with poleward flow 
tend to carry warm water into cooler regions; con- 
versely, equatorward flow carries cool water into warm 
regions. Within the currents themselves the distri- 
bution of density produces a temperature gradient 
such that, in the northern hemisphere, the water on 
the left side of the current has a lower average 
temperature than water on the right side. This may 
be reflected by a thinner mixed layer or even by 
lower surface temperatures. In the southern hemis- 
phere the structure is reversed. 

Divergence and Convergence of Surface 
Currents 

Divergence of the surface currents may occur under 
the influence of the wind. Examples of this effect are 
found along the western coasts of the continents and 
in the vicinity of the equator in the eastern parts of 
the Atlantic and Pacific. In these areas upwelling 
brings water towards the surface from moderate 
depths and the thermocline may be shallow or, in 
extreme cases, absent. The opposite effect, namely 
convergence, occurs in the center of the subtropical 
gyrals in the northern and southern hemispheres. 
In these regions the surface water accumulates and 
consequently the thermocline may be very deep. 

Tidal Currents 

Tidal currents in partially isolated, shallow areas 
have a marked effect on the temperature conditions 
because they also cause turbulent mixing. In areas of 
strong tidal currents, for example in the English 
Channel, the water may remain virtually mixed 
throughout the year, although there is, of course, 
heating and cooling of the water column as a whole. 

Internal Waves 

Internal waves also affect the temperature distribu- 
tion. The effect of these waves is reflected in a periodic 
rise and fall of the thermocline. Periods as long as 12 
and 24 hours are known to exist, and recent studies 


have shown that waves of only a few minutes period 
may occur. Whether there is a continuous spectrum 
of frequencies is not known. An example of the effects 
of internal waves on temperature structure is shown 
in Figure 12. 

4 4 GEOGRAPHICAL VARIATIONS 

4.4.1 Dependence of the Annual Cycle on 
Geographical Location 

The annual cycle in temperature conditions repre- 
sents the net effect of the annual sequence in the 
various factors described, particularly in the amount 
of radiation received, the heat losses associated with 
evaporation, and the character of the prevailing 
winds. In low latitudes where these factors do not 
vary appreciably there is little change in conditions 
throughout the year, except that near the continental 
boundaries changing monsoon winds may introduce 
variable conditions. 

It is in the latitudes of 40° to 50° that the annual 
cycle is most conspicuous. This is to be expected, 
since in these regions the surface experiences the 
greatest range of temperature. The effects of this 
great variation in temperature are magnified by the 
fact that in winter the cooling due to low tempera 
tures is increased by the greater evaporation that 
occurs at this season; the resultant increase in the 
density of the surface water facilitates mixing and 
thus contributes to the seasonal variation. The typi- 
cal cases shown in Figures 4 and 5 illustrate this 
point; they are based on observations in the open 
ocean in an area of relatively strong winds, far from 
land and where salinity changes are relatively small. 
The annual cycle is even more pronounced in regions 
near land, or in areas where heavy precipitation 
occurs and light winds are prevalent during the 
spring and summer. These conditions tend to induce 
even more extreme negative gradients than those 
shown in Figure 4. This can also be observed gener- 
ally in areas of flow towards the equator, in which 
cool water is being heated ; an example of this is the 
region off the California coast. 

442 Dependence of the Diurnal Cycle on 
Geographical Location 

The diurnal change in temperature gradients is 
essentially similar in principle to the annual cycle, 


80 


THE OCEANOGRAPHY OF SOUND CONDITIONS 


TIME 



Figure 12. Effects of internal waves on temperature structure. (A) Internal waves shown by the progressive variation 
of depth at which a given temperature exists. The experimental points are plotted at the depths at which the middle 
of the thermocline occurred, as indicated by the vertical dotted lines adjacent to the bathythermograms. (B) Internal 
waves from bathythermograph readings at 2-minute intervals, and the smoothed curve. 


but the temperature changes are smaller and do not 
extend to such great depths. The incoming solar 
radiation depends upon latitude, time of year, time 
of day, and the cloudiness. The diurnal cycle of in- 
coming radiation changes during the year, the varia- 
tion being least near the equator and increasing 
towards the poles. Above the polar circles, of course, 
there are days of complete darkness during the 
winter and continuous daylight during the sum- 
mer. It should be recognized that the diurnal 
change is not necessarily cyclic, as is the annual 
change, and that progressive heating or cooling of 
the water will be characteristic in middle and high 
latitudes. Within the tropics where the annual 
variation is small, the diurnal changes are more 
nearly cyclic. 


Even if the total heat absorption be the same, the 
character of the changes in temperature gradients 
may be quite different, since these depend upon the 
previously existing gradients and on the wind con- 
ditions. A negative gradient near the surface will be 
increased by incoming heat unless a strong wind 
(force 4 or greater) springs up. On the other hand, 
the changes in an initially mixed (isothermal) layer 
will depend critically upon the wind strength. De- 
velopment of surface gradients is common when the 
wind force is 3 or less but is rare with winds above 
force 4 (see Figures 6, 8, and 11). In the tradewind 
belts, therefore, development of surface gradients 
during the day is a rather rare condition; this is 
probably another factor to be considered in explain- 
ing Figure 11. 



GEOGRAPHICAL VARIATIONS 


81 


443 Summary 

The regional differences in temperature structure 
can be explained in terms of the factors described. 

The discussion can be summed up as follows : 

An isothermal layer near the surface is the result of 
mixing. The factors inducing mixing are (1) wind, 
(2) radiative cooling, (3) evaporation, with its conse- 
quent cooling and salinity increase. 

Strong negative gradients are the effect of heating 
a stable surface layer, without much wind mixing. 


Strong winds may more or less prevent the forma- 
tion of negative gradients. 

Positive gradients are produced only in areas where 
cool, dilute water flows, or is formed, on top of 
warm, more saline water. Measurable positive 
temperature gradients are most common during 
the fall and winter months in the northwestern 
Atlantic and Pacific oceans, where cold, dilute 
coastal waters are driven offshore by the wind 
and flow over the warm but saline ocean water of 
higher density. 


Chapter 5 


ECHOES, SCATTERING, AND REVERBERATION 


5 i THE GENERAL NATURE OF 
REVERBERATION IN THE SEA 

W hen A short tone pulse is sounded in a large, 
empty room, the sound echoes and re-echoes 
from the walls, ceiling, and floor for a considerable 
time. This phenomenon is called reverberation. It 
has been studied extensively by acoustic engineers, 
because it interferes with the understanding of 
speech and the enjoyment of music. Suitable wall 
covering deadens the room and eliminates reverbera- 
tion. 

When an echo-ranging pulse of sound is emitted 
into the ocean, a very similar phenomenon is ob- 
served, and the name “reverberation” was early 
applied to it. However, while the ocean has a floor 
and a ceiling, it lacks the four walls of a room, and 
both the laws and the causes of underwater reverber- 
ation are somewhat different. 

Theoretically, if the sea surface and bottom were 
mirror-flat and if there were no suspended matter 
(including fish) in the water, there would be no 
reverberation. Every departure from these ideal con- 
ditions results in an echo, usually a very weak echo. 
However, there are very many irregularities on the 
ocean bottom, and each wavelet on the surface prob- 
ably contributes its individual echo. The combined 
result is a scattering of sound in all directions. Some 
of this scattered sound comes back to the transducer, 
and is heard in the sonar loudspeaker. It is the 
reverberation. 

Reverberation is therefore to be considered as the 
resultant of a large number of very weak echoes. 
Some of the targets producing these echoes are not 
very obvious nor is very much known concerning 
them. They may be air bubbles, suspended solid 
matter, organic matter such as plankton and the fish 
feeding on plankton, or minute inhomogeneities in 
the thermal structure. On the other hand, minor ir- 
regularities of the ocean bed are very effective scat- 
tered, and when the sound beam strikes the bottom 
reverberation is very high. The surface waves un- 
doubtedly contribute appreciably to it. 

Reverberation is easily distinguished from extrane- 
ous noise because it is a tone of fairly definite pitch, 
whereas noise has a wide band of frequencies. The 


individual echoes mentioned above as forming the 
reverberation are not perceptible as such ; they over- 
lap each other in time, causing marked fluctuations 
in the intensity. If the signal is of constant frequency, 
transmitted horizontally, it is succeeded by a quaver- 
ing, ringing tone of rapidly decreasing loudness, 
interspersed with very occasional bursts of sound that 
might be mistaken for echoes by an inexperienced 
observer. In shallow water a crescendo effect may be 
perceived after a certain interval due to sound scat- 
tered backward by the bottom. 

If relatively long pings (of about 200-msec dura- 
tion) of constant frequency are used, reverberation 
has a musical sound. With shorter pings, the musical 
character disappears ; although pitch can still be dis- 
tinguished, the tone becomes rough and grating. 

When a frequency-modulated signal is used, the 
reverberation is quite accurately described by compar- 
ing it to the clatter made by coal sliding down a metal 
chute. Some frequency modulation may occur because 
of improper functioning of the sonar oscillator. If 
the reverberation from long pings of supposedly con- 
stant frequency is not musical, the oscillator should 
be examined by a competent maintenance man. 

The pitch of the reverberation from a constant- 
frequency ping depends on the speed of the echo- 
ranging vessel and the relative bearing of the 
projector. 

While this description of reverberation has been 
linked to the operation of echo ranging, the phenome- 
non occurs whenever sound is transmitted through 
the sea. The reverberation “tails” visible on Figure 
52 of Chapter 3 have already been mentioned and 
will be more fully discussed below. 

The mechanism of scattering or reverberation, 
and the mechanism of echo formation are very 
similar. It is convenient to discuss them at the 
same time. 

In the sections that follow we shall consider first 
the formation of echoes and then apply the principles 
to echoes from small solid and liquid particles and 
from bubbles, and we shall also devote some attention 
to the scattering of sound from nonspherical objects 
(Section 5.2). This will be followed by an empirical 
discussion of reverberation in the ocean (Sections 
5.3 and 5.4). 


82 


THEORY OF SCATTERING BY SINGLE PARTICLES 


83 


THEORY OF SCATTERING BY 
SINGLE PARTICLES 


5.2.1 Elementary Theory of 

Echo Formation 

When a sound wave passes over an obstacle sus- 
pended in the medium, the latter is set into vibration 
and becomes a secondary source of sound. The ampli- 
tude of the vibration is proportional to the amplitude 
of the primary sound, and consequently the intensity 
of the secondary sound is also proportional to the 
primary intensity. 

The simplest case to consider is that of an object 
like a submarine or a large fish, with dimensions 
which are large compared to the wavelength of the 
sound. This intercepts a certain amount of sound and 
casts an acoustic shadow. The intercepted power is 
reradiated as the secondary sound or, as it is more 
usually called in this case, the echo. 

Target Area 

The amount of power intercepted is determined 
by the target area of the obstacle. For the present, the 
target area may be defined in a picturesque manner 
by imagining a shadow cast by the obstacle to fall on 
a plane perpendicular to the sound rays. The shaded 
area is the target area a. In the case of a sphere of 
diameter d, for example, it follows that the target 
area would be a circle of area 

<t= z \i rd 2 . (1) 

In the case of irregular objects, the target area will de- 
pend on the direction from which the sound is incident. 

Let F be the energy flow (in w/unit area) at the 
obstacle and W the total power intercepted. Then 
W = Fa. (2) 

If the target is perfectly reflecting, all this energy is 
reradiated as sound. If the target is not perfectly 
reflecting, only a fraction, a, of this energy will be 
reradiated. Thus the secondary sound power will be 
W, = Fxa. (3) 

The effect of absorption is thus the same as if the 
target area were reduced in the proportion a. This 
secondary sound is radiated in all directions, though 
not necessarily equally in all directions. 

A large rigid plane would reflect the secondary 
sound into a single direction, like a mirror; such mir- 
ror-like targets almost never occur in the sea. The sea 


surface is perhaps the closest approach to such a tar- 
get, but even the sea surface has properties different 
from those commonly associated with a mirror. It may 
be sufficient to recall the way in which the sun and 
moon are reflected by the sea surface ; it reflects sup- 
ersonic sound in an analogous manner. 

A sphere reradiates the sound equally in all di- 
rections and is thus the simplest case to treat. It may 
seem that the existence of a shadow is in contradiction 
to this statement; however, at great distances from 
the sphere, diffraction causes the shadow to disap- 
pear. Consequently, the statement is strictly correct 
only at a considerable distance from the spherical 
target. This is discussed in detail in the appendix to 
this chapter. 

At a great distance r the power W s that is reradiated 
from the target, flows through the whole area r 2 
of an imaginary spherical surface centered at the tar- 
get. Hence the energy flow of the secondary sound is 


F<xa 

47rr 2 ’ 


(4) 


or, in the case of a sphere 


F s 


Tad 

lfh 2 ’ 


(5) 


If the target is not spherical, it will radiate more 
sound in some directions and less in others than is 
predicted by equation (4) . But this equation will still 
be valid, on the average. The target area a already 
depends on the direction of the incident sound ; by a 
slight generalization, we may consider it also to 
depend on the direction in which the sound is scat- 
tered and on the reflecting properties of the target 
as well and thus take into account these variations 
of F s with sound direction and target reflectivity. 
Target area is then defined by the equation 


Fa 

p = 

s 47rr 2) 


( 6 ) 


and the picturesque definition given above no longer 
applies. This abstract definition of a is the more 
useful of the two. 


Intensity of the Scattered Sound 


Since the energy flow F is in this case proportional 
to the intensity I ( =p 2 ) (see Section 1.2), equation 
(6) may also be written 


la 

47rr 2 ' 


( 7 ) 


84 


ECHOES, SCATTERING AND REVERBERATION 


It should be noted that, in this equation, r is the 
distance from the target to the point at which the 
scattered intensity is being calculated. The primary 
intensity itself, 7, will depend on r', the distance 
from source to target, and in the general case r’ will 
not equal r. Neglecting refraction (this has been 
implicit in all of the above), equation (11) of Section 
1.2 is applicable: 


Therefore 



47rrV 2 


(8) 


If the echo is received at the source of the sound, as 
in practical echo ranging, r = r', and hence 



(9) 


Echo Level and Target Strength 

The echo intensity is generally measured at the 
source, in decibels; this is called the echo level E and 
is defined by 

E = 10 log I s . (9a) 

Taking logarithms of both sides of equation (9), 

E = Li + T — 40 log r, (9b) 

where 


and 


L\ = 10 log Ji, 
T= 10 log j. 


(9c) 


The quantity T, defined in this way, is called the 
target strength of the scatterer. It gives a quantita- 
tive idea of the reflecting characteristics of the target 
and is a very useful concept. 


5 . 2.2 Echoes from Small Particles 

The phenomenon of scattering or reverberation 
differs from echo formation only in that it results 
from the action of many relatively small targets 
rather than from one large target. The action of a 
single scatterer can still be described by equation (9) . 

The picturesque definition of target area fails 


completely when the scatterer has dimensions which 
are less than the wavelength of the sound. The target 
area, or the effective cross section , of small solid or 
liquid particles is much less than their actual cross 
section, in a ratio which is roughly (x d/X) 4 , d being 
the diameter of the particle and X the wavelength of 
the sound. This result was first obtained by Rayleigh 
but has since been studied by many others. The 
effective cross section also depends on the density 
and elasticity of the particle and the medium. 

Figure 1 illustrates the variation of target area 
with wavelength for the two extreme cases of a heavy, 

7 TdA 



Figure 1 . Variation of target area with wavelength, in 
the case of small bubbles and heavy, rigid spheres. The 
ratio of the target area a to the actual cross-sectional 
area I^xd 2 is plotted as a function of the ratio of the 
circumference of the scatterer ird to the wavelength X 
of the sound. 

rigid sphere and an air bubble. The ratio of the 
target area <r to the actual cross-sectional area 4xd 2 
is plotted as a function of xd/X, which is the ratio of 
the circumference of the scatterer to the wavelength 
of the sound. When the latter is greater than 2, both 
curves coincide and show oscillations about the mean 
value of unity for the ratio 



THEORY OF SCATTERING BY SINGLE PARTICLES 


85 


Where 7 rd/\ is greater than 10, both curves indi- 
cate that the target area is practically equal to the 
actual area. For values of t d/\ less than unity, the 
two curves differ markedly. 

In the case of a heavy, rigid sphere, the graph 
slopes off sharply when 7 rd/\ is less than unity. The 
graph for a gas bubble first rises to a very large value, 
reaching a maximum at a value of 7rd/X = 0.012, and 
then drops rapidly for smaller values. This difference 
in the behavior of bubbles and other scatterers will be 
discussed in detail in the next two sections. 


5.2.3 Target Area of Small Solid or 
Liquid Scatterers 


The equation of the lower part of the curve for a 
heavy, rigid sphere was worked out by Rayleigh. 1 
It is 


V 4 
\ird 2 ~ 9 


mV 

(-) «V+KV), 


( 10 ) 


where 

d = diameter of sphere, 

X = wavelength of sound, 

Co, Ci = constants depending on the density and 
elasticity of the particle. (See Table 1.) 


than unity, in the case of the latter, somewhat less. 
Thus, for a given diameter and wavelength, the 
equation shows that a balsa-wood sphere scatters 
about ten times as much sound power as a clay sphere, 
while a globule of turpentine scatters only about 
one-sixth as much as the clay. 

The scattering power of a small object is much 
more profoundly affected by its size and the wave- 
length of the sound. For 24-kc sound, X = 3 in., approxi- 
mately. Hence a sphere greater than 30 in. in cir- 
cumference will have a value of xd/\ that is greater 
than 10. The graph shows that such a sphere will 
have a target area equal to its actual cross section. 
Rayleigh’s equation will apply only to spheres with a 
circumference less than 3 in. A simple calculation 
shows that the target area of a sphere 0.3 in. in 
circumference will be only one-millionth that of a 
sphere 3 in. in circumference. This is also the ratio 
of the sound power scattered by the two. 

A small sphere will scatter less sound of long wave- 
length than of short. For example, the wavelength of 
2.4-kc sound is ten times that of 24-kc sound; the 
equation shows that a small, solid sphere will there- 
fore scatter 10,000 times more sound of 24-kc fre- 
quency than of 2.4-kc frequency. This marked de- 
pendence on frequency is very characteristic of 
scattering by small objects. 


Table 1 . Values of the parameters Co and C h equation 
(10), for various substances when suspended in sea 
water. 


Substance 

Co 

Cr 

Iron 

0.99 

0.81 

Clay 

0.93 

0.50 

Granite 

0.98 

0.57 

Marble 

0.94 

0.53 

Wood (balsa) 

-3.5 

-0.50 

Wood (iron wood) 

-0.87 

-0.25 

Turpentine* 

-0.43 

-0.07 


* Included as an example of an organic liquid, without implying 
that it might occur in the ocean. 


For simplicity, only the average value of a is given, 
and the dependence on angle is ignored. The value 
of the factor 

♦(W + KV) 

is not much different from unity for most substances. 
Table 1 lists the values of C 0 and Ci for several sub- 
stances, and it is seen that only balsa wood and 
turpentine provide exceptions to this statement. In 
the case of the former, the factor is somewhat greater 


5.2.4 Target Area of Bubbles 

It is difficult to understand how bubbles can exist 
permanently in the sea, since sea water is not sat- 
urated with air except very near the surface. There 
are several obvious sources of intermittent bubble 
formation: whitecaps; the breaking of the bow wave, 
which causes bubbles to be washed under a ship and 
into its wake; the rotation of the propellers of ships 
or submarines, even when the latter are submerged. 
There are thus occasions when air or vapor bubbles 
might be expected to exert an appreciable influence 
on the transmission of sound. This was first investi- 
gated by H. F. Willis, of H. M. A/SEE. The dis- 
cussion and the equations which follow are based on 
work of the staff of CUDWR. 5 - 6 

A gas bubble is much more compressible than the 
surrounding water. Under the influence of a sound 
wave, it will therefore pulsate with a relatively large 
amplitude. In order to follow the pulsation, the water 
immediately surrounding the bubble must oscillate 
with an amplitude considerably greater than that of 


86 


ECHOES, SCATTERING AND REVERBERATION 


the water at a distance. The mass of this surrounding 
water coupled with the compressibility of the air 
results in resonance at a frequency / 0 which depends 
on the diameter of the bubble d and on the average 
pressure P of the gas in the bubble. The dependence 
on P arises because the compressibility of a gas de- 
pends on its pressure. An approximate formula for 
the resonant frequency is 



p being the specific gravity of the medium. When/ 0 
is in kilocycles, d in inches, and P in feet of water 
this becomes 

fod = 0.02P K (12) 

For example, at a depth of 66 ft, P = 100, since the 
atmospheric pressure at the surface of the sea is 
about 34 ft of water. Hence, at this depth, f 0 d = 0.2. 
A 1-in. bubble thus resonates at 0.2 kc and a 0.01-in. 
bubble at 20 kc. For a bubble at the surface, P = 34 ft, 
so that fod = 0.12. Since frequency is inversely pro- 
portional to wavelength, this is equivalent to the 
equation 

7T d 

— = 0 . 012 , 

Ao 


where A 0 is the wavelength corresponding to the 
resonant frequency / 0 . 

The graph for bubbles in Figure 1 shows a sharp 
maximum just at this value; it is caused by the high 
amplitude with which the bubble vibrates when 
sound of the resonance frequency is incident on it. 

The sharpness of the resonance peak of the bubble 
is determined by a parameter Q, analogous to that 
familiar in the theory of electrical circuits. The value 
of this parameter cannot readily be calculated, but 
is certainly less than A 0 /d. Experiments by Carsten- 
sen and Foldy indicate that the empirical formula 


Q = 


17.5 

i+7/io 


(13) 


is valid in the range / = 5 to 35 kc. 6 

For sound frequencies near resonance, the effec- 
tive cross section of a bubble becomes very large 
(<r = 7t d 2 Q 2 , approximately) and may approach A 0 2 . 
Thus at a depth of 65 ft a bubble 0.01 in. in diameter 
has a target area of several square inches for 20 kc 
sound. This surprising result comes about because 
of the high amplitude of oscillation of the bubble, 


which causes it to reradiate a large amount of second- 
ary sound. It is difficult to calculate the exact value 
of the effective cross section for the resonance fre- 
quency, and experimental evidence is not exact. 

For frequencies more than an octave above reso- 
nance, the target area is about equal to the actual 
cross section of the bubble. 

For frequencies more than an octave below reso- 
nance, the target area is considerably less than the 
actual cross section, and can be approximately calcu- 
lated from equation (8) with 

Co = - 450P, 

(14) 

C x =- 2.0. 

Comparing these values with those of Table 1, it is 
seen that gas bubbles scatter low-frequency sound 
considerably more effectively than do solid particles 
of the same size. This is also shown by Figure 1. 


5.2.5 Target Area of Nonspherical 
Objects 

The mathematical investigations just discussed 
have been confined to the case of spheres. Their ex- 
tension to nonspherical objects is not simple, but has 
been carried out for some cases. 7 It is clear that the 
same general laws will govern the more general 
shapes. For example, a fish that is not too flat or 
elongated will cast a shadow roughly equal in area 
to that of a sphere of the same volume. This estimate 
may be in error by a factor of 2 or 3, but it is unlikely 
to be in error by a factor of 10. Another uncertainty 
in the calculation is caused by our ignorance of the 
reflection coefficient. This will depend largely on the 
compressibility of the fish. If the fish has a swim 
bladder (air cavity) this will probably be the most 
effective portion in reflecting sound. Similar remarks 
apply to kelp and other forms of marine life. As is 
well known, these plants have gas-filled floats, and 
are therefore very good reflectors of sound. 

The bottom is especially important in the produc- 
tion of reverberations. Boulders, pebbles, shells, 
coral, etc. are all potential scatterers of sound. A 
smooth sand or mud bottom will theoretically be- 
have more or less like a mirror, and scatter little sound 
back to the source. The experimental facts in this 
connection will be discussed below. 

The waves on the sea surface will also act more or 
less like separate targets. The large surfaces will re- 
flect supersonic waves more or less like curved mir- 


THEORY OF REVERBERATION 


87 


rors. The effect of the smaller ripples is not clearly 
understood, but they will probably scatter the sound 
more or less equally in all directions. 

5.3 THEORY OF REVERBERATION 


5 . 3.1 General Ideas of the Theory 

None of the small scatterers just discussed would 
return an appreciable echo by itself. As has been in- 
dicated, it is the simultaneous reception of the echoes 
from a large number of them that constitutes what 
we call reverberation. 

Train Length 

To understand the manner in which the scatterers 
cooperate in producing reverberation, one must con- 
sider the manner in which a pulse of sound (a “ping”) 
is propagated. If the duration of the pulse is U sec- 
onds, it will consist of a train of waves whose total 
length is d 0 , c being the velocity of sound. This 
distance will be called the train length of the pulse. 
Since c = 1,600 yd/sec, approximately, a pulse of 
duration 0.1 sec ( = 100 msec) will result in a wave train 
160 yd long. If the frequency is 24 kc, there will be 
24,000 X 0.1 = 2,400 complete waves in the train. 

Ping Length 

One-half the train length is called the ping length ; 
a pulse lasting 0.1 sec thus has a ping length of 80 yd. 
The ping length is a more useful concept than the 
train length, for two reasons. In echo ranging, the 
time required for the pulse to travel from projector to 
target and back to the receiver is measured. The 
clock is the range dial and is calibrated in terms of the 
range of the target that returned the echo, not in 
terms of seconds. If a target is at range r, the travel 
time is 2 r/c. Therefore, if the echo is a pulse of dura- 
tion t 0 , the range indication will increase by the 
amount r 0 = cto/2 during the reception of the echo. 
This is just the ping length as defined above. 

In the second place, if there are many targets or 
scatterers, the echoes that are heard simultaneously 
come from those scatterers for which distances from 
the sonar differ by less than r 0 . At a given instant, 
therefore, echoes will be received from all scatterers 
that lie in a spherical shell, with a thickness r 0 , as 


shown in Figure 2. At this instant, the actual train 
of waves will no longer be passing over this particular 
lot of scatterers; it will have moved onward during 
the time the echoes were returning to the sonar. The 
instantaneous relation between the volume A, from 



Figure 2. Diagram showing the instantaneous relation 
between the regions from which echoes are being 
heard (A) and the volume occupied by the wave train 
(B), in the case of a beam whose angular half width 
is a radians. 

which the echoes are being heard, and the volume B 
that is occupied by the wave train, is shown in 
Figure 2. 

This figure also shows graphically how the ping 
length and train length are related. Very little further 
reference will be made to the train length, as almost 
no interest centers on the region B. On the contrary, 
frequent reference to region A will be needed, and 
these will bring with them references to the ping 
length. 

5 . 3.2 Intensity of Volume Reverberation 

The effect of scatterers suspended in the volume 
of the sea can now be calculated. Consider the sim- 
plest possible case : 

1. There are N scatterers per unit volume. 

2. Each scatterer has the target area <r. 

3. The sonar has a sharply defined beam of half- 
width a, its directivity pattern being as shown in 
Figure 3. 

4. The sonar is in such a place that all effects of 
surface and bottom can be ignored. 

The intensity of the echo from a single scatterer 
will be given by equation (9), provided it is in the 
beam, and will be zero otherwise. There will be many 
scatterers in the active shell (region A, Figure 2) at 
any instant. If V is the volume of this region, the 


88 


ECHOES, SCATTERING AND REVERBERATION 



Figure 3. Diagram illustrating an ideal beam pattern 
of half width a. The dotted line represents the axis 
of the beam. 


number of scatterers whose echoes are being received 
will be NV. Combining this with equation (9), the 
intensity of the reverberation will be 


hNVa 
4ir r 4 


(15) 


Now the volume V is easily calculated. It is given 
approximately by 

V = 27rr 2 r 0 (1— cos a), (16) 


where r is the range to the center of region A . Hence 
finally 


Ir = I\ 


(N err 0 )(1 — cos a) 
2r 2 


(17) 


A number of conclusions can be drawn from this 
equation, as will be seen in the following chapters. A 
brief list of the simpler conclusions follows. 

1. The reverberation intensity Ir is proportional 
to the source intensity Ii: increased sound output 
increases the reverberation. 

2. The reverberation is proportional to the ping 
length r 0 : a long ping causes more reverberation than 
a short one (see Figure 4). 

3 . Since ( 1 — cos a) increases as a increases, it is seen 
that a broad beam causes more reverberation than a 
narrow one. In general, doubling the width of the 
beam will cause Ir to increase about fourfold. 

4. The (volume) reverberation intensity varies 
inversely as the square of the range r; this should be 
compared with equation (9), which shows that the 
echo from a single target varies inversely as the 
fourth power of r. The reason for the difference is the 
increase in the active volume V (region A) as r in- 
creases. 



Figure 4. Data showing relation between ping length 
and reverberation intensity. If the latter were strictly 
proportional to the ping length, the dots would lie on 
the solid curve. 


5.3.3 Intensity of Surface and 

Bottom Reverberation 

The theory of volume reverberation, as presented 
in the previous section, requires only slight modifica- 
tions when the scatterers are located on either the 
surface or the bottom. These two cases are, in many 
ways, identical. Instead of an active volume V, one 


VERTICAL SECTION 




Figure 5. Similar to Figure 2, showing active areas 
on surface and bottom for two different positions of 
the wave train. 

must deal with an active area A, namely, the area of 
the intersection of the surface (or bottom) with the 
region A of Figure 2, already discussed. In Figure 5, 


THEORY OF REVERBERATION 


89 


two successive locations of the active volume are 
shown. Until the beam intersects the bottom, there 
is no active area on the bottom; at position 1, there 
is an active area -on the surface, but none on the bot- 
tom. After some time, position 2 is reached and there 
is an active area on the bottom as well as on the 
surface. The figure is drawn for the case of a sonar 
mounted on a surface vessel; if the sonar were on a 
submarine near the bottom, the situation would be 
reversed. Note that at very short range there is no 
active area on either bottom or surface; this is shown 
in greater detail by Figure 6. 


RANGE 



Figure 6. Graph showing variation of active areas 
on surface and bottom as a function of range, for the 
case where the projector is very close to the surface. 


a. Consequently, doubling the width of the beam 
increases surface reverberation only by a factor of 
two rather than four. Finally, surface reverberation 
varies inversely as the third power of the range, while 
volume reverberation varies as the inverse second 
power. 

If the range is not great enough so that equation 
(18) can be used, somewhat more elaborate calcula- 
tions are needed. The first three conclusions concern- 


RANGE 



Figure 7. Dependence of surface and bottom re- 
verberation on range. It is assumed that the scattering 
coefficient is the same for both surface and bottom. 
Actually this number is much greater for the bottom 
than for the surface. This results in shifting the graph 
of bottom reverberation upward relative to the surface 
graph. 


The mathematical expressions for the active areas 
are rather complicated, except in the special case 
that the projector is very close to the surface. Then 


A = 2 ar 0 r, 


(18) 


where a is to be expressed in radians. The graph of 
this equation is shown as a dotted line on Figure 6. 
The departures at short ranges are obvious. 

It will be assumed, for simplicity, that there are 
N' scatterers per unit of active area and that each 
scatterer has the target area <r. Then the intensity 
of reverberation is [compare equation (15) ] 


7i N'A<r 

Ir = . 

4tt r 4 


(19) 


If the range r is great enough so that equation 
(18) can be used for A, 


I]N'ar 0 (x 
2tt r 3 


( 20 ) 


Conclusions (1) and (2) given above apply to this 
equation also. The third conclusion requires only 
slight modification, because (1 — cos a) is replaced by 


ing volume reverberation apply without appreciable 
change, however, and only the dependence on range 
is changed. The graphs of Figure 7 show this de- 
pendence on range for surface and bottom reverbera- 
tion. In this Figure it has been assumed that N f , the 
number of scatterers per unit area has the same value 
for both surface and bottom. Actually N' has a much 
greater value for the bottom than for the surface. 
This results in shifting the graph of bottom reverbera- 
tion upward relative to the surface graph. 

Figure 8 shows comparative levels of an echo from 
a single target, of volume reverberation, and of surface 
(or bottom) reverberation, as calculated from equa- 
tions (9), (17), and (20), respectively. In order to 
give a standard of comparison, it is assumed that all 
three have the same level at 1,000 yd, which will not 
necessarily be the case in practice. It will be noted 
that, at shorter ranges than 1,000 yd, the levels 
increase in the order volume reverberation, surface (or 
bottom) reverberation, echo. At longer ranges, they 
decrease in this same order. The graphs diverge 10 db 
from their neighbors for each tenfold increase or 
decrease in range. 


90 


ECHOES, SCATTERING AND REVERBERATION 



Figure 8. Comparative levels of (A) echo from a single 
target, ( B ) surface (or bottom) reverberation, (C) 
volume reverberation. In order to give a standard of 
comparison, it is assumed that all three have the same 
level at 1,000 yd, which will not necessarily be the 
case in practice. 


It should also be remembered that Figure 8 is 
quite schematic as far as surface and bottom rever- 
beration are concerned and should be modified in 
accordance with Figure 7. 


5.3.4 Extension of the Theory to 
Nonideal Conditions 

All of the preceding calculations have been based 
on a number of simplifying assumptions that cannot 
be expected to be correct under actual conditions, 
but are useful in presenting the basic ideas. The com- 
plications introduced by departures from the ideal 
cases just examined will now be considered. 


Scattering Coefficients 

The first simplification was that the scatterers all 
had the same target area a and that there were N of 
them in each unit volume (or N' on each unit area). 
Obviously, the scatterers will not all be the same, but 
since only the combination Na enters the final equa- 
tion, this does not cause any particular trouble. It 
is seen that m = Na is the total target area of all the 
scatterers in a unit volume. This quantity is called 
the volume-scattering coefficient. Since N is measured 
in yd ~ 3 and o’ in yd 2 , mis measured in yd -1 ; that is 1/m 
is a length. It is essentially the distance a wave train 
can travel before much of its energy is scattered. 

In the same way, n = N'a is the total target area 
of all the scatterers located on a unit area ; it is called 
the surface- or bottom-scattering coefficient. Since N' is 
measured in yd ~ 2 and a in yd 2 , n will be dimensionless, 


i.e., it will have the same numerical value whether 
yards or feet are used as units. 

Replacing No- by m and N’a by n will remove this 
oversimplification from equations (17) and (20). 


Beam-Pattern Correction 

The second simplification is the assumption that 
the projector emits the sound in a sharply defined 
beam, with no sidelobes. When actual projectors are 
involved, the factor (1 — cos a) in equation (16) and 
the factor a in equation (18) must be replaced by 
others, the exact values of which depend on the beam 
patterns of the projector. Call these factors K v and 
K s , respectively; equations (17) and (20) then become 


hK v mr 0 

(volume reverberation), 

(21) 

r 2 

IiK s nr 0 

(surface reverberation) . 

(22) 

2 r 3 


The two factors K v and K s , like the ones they re- 
place, bear a simple relation to the half-width of the 
main lobe of the transducer. 8 Let a be redefined as 
the angle (in degrees) at which the beam pattern has 
a value 6 db below the maximum (or axial) level. 
Then the values of K s and K v are given approxi- 
mately by the equations : 

K s = 4.2 X 10 _3 a, (23) 

K v = 4ttK s 2 = 5.5 X 10 -5 a 2 . (24) 

It should be noted that the scattering coefficients 
are independent of the projector, whereas K s and K v 
are independent of the ocean. 

Reverberation Levels 

Finally, it has implicitly been assumed that the 
sound rays are straight lines, and that the inverse 
square law determines the whole transmission loss. 
In actual cases, the departures from these ideal laws 
introduce marked effects, which can be ascribed to 
departures from the inverse square law of transmis- 
sion loss. 

In order to deal with these complications in as 
simple a manner as possible, it is convenient to de- 
fine the reverberation level RL by 

Ir 

RL = 10 log — db. (25) 


THEORY OF REVERBERATION 


91 



Figure 9. Oscillograms of reverberation and echo. Range marks are spaced 40 yd apart at the upper edge. 


It will be noted that RL is independent of the sound 
output of the sonar. 

The volume and surface-reverberation indices J v 
and J s are defined by 

J v = 10 log K p , (26) 

J s = 10 log K s , (27) 

and, with these substitutions, equations (21) and 
(22) become 

RL V = J v + 10 log (mr 0 ) — 20 log r (volume), (28) 

( nr 0 \ 

—J — 30 log r (surface). (29) 

These equations are correct only if the transmission 
of sound is accurately given by the inverse square 
law. It can be shown that the departures from the 
inverse square law are in most cases properly taken 
into account in the following equations : 

RL v = J v + 10 log (mr 0 ) — 2H v + 20 log r, (30) 

( nr 0 \ 

— J - 2 H s + 10 log r, (31) 

where H v and H s are the actual transmission losses 
from the sonar to the active regions responsible for the 
reverberation. It is easily seen that if H v = H s = 20 
log r, equations (30) and (31) reduce to equations 
(28) and (29). 

5.3.5 Fluctuation of Reverberation 
Amplitude 

The form of equations (28) and (29) suggests that 
the reverberation decreases steadily with time from 
an initial high level. This is not true. The “ringing” 
sound mentioned earlier in the discussion indicates 


that rapid changes in the intensity occur which are 
not predicted by these equations. The oscillograms 
of recorded reverberation show these changes very 
clearly, as can be seen by an examination of Figure 9. 

These are specimens typical of the experimental 
data in this field and will be discussed in some detail. 
The three oscillograms were taken in rapid succession 
with different ping lengths of 0.8 yd, 8 yd, and 24 yd. 
The electric input to the transducer was coupled to 
the oscillograph and is recorded at the extreme left. 
This is followed by a blank interval of about 0.025 
sec, during which the connections were changed 
from “send” to “receive.” The portions of the trace 
to the right of this are reverberation, except for the 
echo, which is clearly visible in each. The early 
reverberation is so intense that it is off scale in the 
two right-hand cases. The ordinates of the three 
oscillograms are comparable, except that the electric 
circuit for recording the outgoing ping did not 
respond fully to the very short 0.8-yd ping. The 
receiving circuits, however, responded fully to its 
echo. It will be noted that this echo is rather weak, 
but that the other two echoes have the same am- 
plitude. This point will be discussed later. 

The theory presented above asserts that the in- 
tensity of the reverberation should be proportional 
to the ping length r 0 . Consequently, the reverbera- 
tion amplitudes should be proportional to r 0 * so 
that the three oscillograms should show amplitude 
ratios of 1 : 3.2 : 5.5 approximately. It is obviously dif- 
ficult to verify this by a single measurement, because 
of the rapid and irregular fluctuations in the ampli- 
tude of the reverberation. On the average, these 
ratios are quite close. 

A more detailed study of the problem shows that 
the theory developed above refers only to such aver- 
age values, and that there is a good explanation of the 



92 


ECHOES, SCATTERING AND REVERBERATION 


rapid changes in amplitude. Two possible causes im- 
mediately suggest themselves : 

1. The number of scatterers in the active region 
varies as the latter moves outward. 

2. The echoes from the different scatterers inter- 
fere. 

The first of these is easily seen to cause some 
fluctuation, but it is often relatively unimportant as 
compared to the second. If there are many small 
scatterers, only the second cause need be considered. 
As the number of scatterers in the active region de- 
creases, the relative importance of the first cause 
increases. 

One consequence of this is that the second cause 
would dominate in the case of long pings (large 
active regions), and the first, in the case of exceed- 
ingly short pings (small active regions). An inspection 
suggests, however, that even for the 0.8-yd oscillo- 
gram, the second kind of fluctuation is important, 
although some of the long “spines” may be caused by 
single scatterers. It would be interesting to study 
even shorter pings, so that an exact estimate of the 
number of scatterers per unit volume could be made. 
The difficulty of constructing transducers with suf- 
ficiently short response times has hitherto prevented 
such work. For longer ping lengths, there is no doubt 
that only the second cause is important. 

The theory of fluctuation due to the second cause 
has been developed by Lord Rayleigh and others. 18 
Let A be the rms amplitude of the reverberation; at 
any given instant, the actual amplitude a may be 
greater or less than A. The probability that a is 
greater than some given value x, is 

p=exp (^f)' (32) 

Some values of this probability are given in Table 2. 


Table 2. Probability that the actual amplitude a is 
greater than x. 


p 

x/A 

10 log rr 2 / A 2 

0.90 

0.32 

- 10.0 (db) 

0.50 

0.84 

- 1.6 

0.368 

1.00 

0.0 

0.10 

1.52 

+ 3.6 

0.001 

2.53 

+ 8.4 

0.00005 

3.16 

+ 10.0 


A number of conclusions can be drawn from this 
table. 

1. The reverberation amplitude is greater than its 
rms value about 37 per cent of the time, and less than 


its rms value 63 per cent of the time. There is thus a 
marked tendency for the reverberation to be below 
the rms value at any given time. The median value is 
84 per cent of the rms value. 

2. The reverberation is more than 10 db below rms 
10 per cent of the time. 

3. The reverberation is more than 10 db above rms 
only 0.005 per cent of the time, or practically never. 

4. During 80 per cent of the time, the level is be- 
tween — 10 and + 3.6 db, relative to the rms ampli* 
tude. 


io log(x%0,db 



Figure 10. Comparison of observed reverberation 
with the Rayleigh formula. 


The Rayleigh formula was checked against experi- 
mental results 9 ’ 10 shown in Figure 10, which is 
based on several hundred measurements of the rever- 
beration amplitude at various ranges. Some of these 
are shown in the figure as circles; the two sets of 



Figure 11 . High-speed oscillogram showing coherence 
of reverberation. Similar to the oscillograms of Figure 
9 except for the scale; the range marks in Figure 11 
are spaced 2.5 yd apart. 

circles represent two separate sets of measurements. 
The solid curve is the graph of equation (32). The 
experimental points are seen to fall very near the 
theoretical curve. Such close agreement is usually, 
but not always obtained. The reasons for the ex- 
ceptional cases are not known. 

The large fluctuations in the reverberation ampli- 


THEORY OF REVERBERATION 


93 



Figure 12. (A) Oscillogram of unheterodyned (24-kc) reverberation. (B) Oscillogram of the reverberation shown in A 
heterodyned to 800 c. 


tude make it essential to average the results of 
experimental measurement. That is, the theoretical 
values of RL, derived above, are all values of 20 log 
A and not 20 log a. Consequently, the procedure is to 
measure a large number of values of a and to compute 
their mean. This mean differs from A, the rms value, 
by a negligible amount. 10 


5.3.6 Coherence of Reverberation 

While the amplitude of reverberation fluctuates 
widely, its envelope changes more or less gradually, 
as shown in the high-speed oscillogram of Figure 11. 
This is similar to those of Figure 9 except for the scale ; 
the range marks of Figure 11 are spaced 2.5 yd apart. 


94 


ECHOES, SCATTERING AND REVERBERATION 


D 



D ENLARGED PORTION 

1 


tion^ndicatedin C SCill ° gram ° f heterodyned (800 " c) reverberation. (D) Enlarged portion of heterodyned reverbera- 

It is seen that, while the amplitude is constantly is the record of the unheterodyned 24-kc current, 
undergoing small changes, the large changes occur Figure 12B, on which the successive cycles are clearly 
rather gradually. resolved, of the heterodyned 800-c current. Figures 

somewhat greater enlargement of an oscillogram 12C and D show this even more clearly. It is seen 
of leverberation is shown in Figure 12. Figure 12A that the changes occur even during a single cycle of 


THEORY OF REVERBERATION 


95 


signal, length 


REVERBERATION RECORDS., 


p«**»*»o m XO o *x xooow 


— e— * < -o : .<X>:; XC 



0<<WHN>oo«-.'a >C»>c -O x: : I>CC-Do« 


XJZ.:C2:ot <Z> 


-3(H» «»«> 


+-W !Qw»»khn<XM )" 


* 



COHERENCE ANALYSIS 



Figure 13. The coherence of reverberation. The graphs on the right are drawn from calculations based on the oscillo- 
grams. The ping lengths are indicated on the left. The lowest strip (and the corresponding curve on the right) show 
the coherence of echoes instead of reverberation. 


the heterodyne frequency, and distort the wave 
form, particularly when the amplitude is small. 

In general, the major changes require a number of 
cycles, and take place gradually. This is sometimes 
expressed by saying that the reverberation “coheres” 
in “blobs,” the latter term being descriptive of the 
oscillogram rather than of the sound. The “rolling” 
character of the sound, however, is indicated by the 
blobby character of the oscillogram. 

The duration of the blobs tends to be about the 
same as that of the ping or echo. This is shown in a 
qualitative way by the three oscillograms in Figure 
9, each of which was made with a different ping 
length. The quantitative aspects are more clearly 
shown by Figure 13. These graphs were made by 
selecting a number of blobs of reverberation from 
oscillograms made with a given ping length. Each 
blob was measured at a number of points, spaced at 
equal distances from its maximum. The measure- 
ments at a given distance to left or right of the 
maximum were averaged and plotted in Figure 
13. For comparison, the ping length is indicated 
on each. 


The graphs furnish good evidence that the dura- 
tion of the blob increases with ping length and is 
about equal to the ping length. The very longest ping 
shows some departure from this last rule; this may be 
caused by fluctuations in the transmission loss (see 
Chapter 3). 

The coherence of echoes is more pronounced than 
that of reverberation, as can be seen in the lowest 
strip of Figure 12. 

5.3.7 Wave Form of Reverberation 

Reference has already been made to the distorted 
wave form of the reverberation. These distortions 
are most obvious when the amplitude is small, but 
they occur at all times. This is indicated, for example, 
by the difference in amplitude of successive cycles in 
Figures 12 and 12 A. 

A convenient measure of the distortion is the time 
interval between alternate zeros of the voltage. In the 
case of an undistorted wave, all these intervals would 
be the same, and equal to the reciprocal of the 
frequency. 


96 


ECHOES, SCATTERING AND REVERBERATION 


It has been possible to construct an instrument, 
called a periodmeter, to record the interval between 
zeros. 11 It traces a dotted line, for which the height 
above a reference line is a linear function of the inter- 
vals. Examples are shown in Figure 14. The upper 
trace was made with an 800-c sine wave from a stand- 



Figure 14. Periodmeter record, showing distortion 
of wave form. Upper trace was made with an 800-c 
sine wave from a standard oscillator. Lower trace was 
made by recording the same tone on a phonograph 
disk and playing it back. The irregular line of dots 
shows that the speed of the turntable varied sufficiently 
to cause variations of more than 20 c in the frequency 
of the reproduced sound. 

aid oscillator. The lower trace was made by record- 
ing the same tone on a phonograph disk and playing 
it back. The irregular line of dots shows that the speed 
of the turn table varied sufficiently to cause varia- 
tions of more than 20 c in the frequency of the repro- 
duced sound. 

The instrument has been found useful in locating 
troubles in the wave form and frequency of the power 
supply of sonars, which in turn affects the wave form 
and frequency of the reverberation and echo. Figure 
15 illustrates this. Figure 15A shows a fairly good 
wave form, but a moderate change in frequency (less 
than 5 c) from beginning to end of the ping. Figure 
15B shows a large frequency drift, together with a 
periodic frequency modulation. This modulation 
apparently resulted from an overtone of the 60-cycle 
ship’s power. A more complicated type of frequency 



Figure 15. Periodmeter record, showing distortion 
of the wave form recorded in (A) apparently by an 
overtone of the 60-c ship’s power. (B) Shows large 
frequency drift and periodic frequency modulation. 

In (C) a more complicated frequency modulation is 
seen. The cause was not completely determined. 

modulation, the cause of which was never completely 
determined, is shown in the lowest trace, Figure 15C. 

Under good conditions (very strong echoes) the 
echo practically reproduces the frequency modula- 
tion of the current supplied to the sonar projector, 
as shown in Figure 16. 


THEORY OF REVERBERATION 


97 



Figure 16. Periodmeter record of an echo. The echo 
is seen to reproduce the frequency modulation of the 
current supplied to the projector. 


Reverberation shows much wider changes in the 
values of successive periods, as shown in Figure 17. 
Some caution must be exercised in interpreting these 
traces in terms of frequency. They are indicative of 
the distorted wave form and are caused by the irregu- 
lar amplitude, as well as by the frequency modulation 
(see Figure 12A). 



VOLUME REVERBERATION 

A 



Figure 17. Periodmeter records of reverberation, 
showing changes in the values of successive periods. 

(A) shows volume reverberation; (B), bottom rever- 
beration. They are indicative of the distorted wave 
form, and are caused by the irregular amplitude as 
well as by the frequency modulation. (See Figure 12A.) 

When the echo is comparable to the reverberation 
in intensity, the periodmeter yields traces like those 


in Figure 18. The trace A shows an echo with no 
doppler, as well as reverberation. The greater stabil- 
ity of the wave form of the echo is apparent. Trace 



t _f 

ECHO 


A 



ECHO 


B 

Figure 18. Periodmeter traces of echoes comparable 
in intensity with the reverberation. (A) shows an echo 
with no doppler, as well as reverberation. (B) shows 
an echo whose frequency has been shifted by doppler 
effect. The large but fairly regular changes in the row 
of dots are caused by beats. 

B shows an echo whose frequency has been shifted 
by doppler effect. The large but fairly regular changes 
in the row of dots are caused by the well-known 
phenomenon of beats. 

There is a widespread opinion that the pitch of 
reverberation rises as the range increases. To test 
this, the periodmeter records were interpreted as an 
indication of frequency (thus ignoring the caution 
mentioned above) and plotted as shown in Figure 
19. Some of the very rapid and irregular changes 
were eliminated by averaging the records over 100- 
msec (80-yd) intervals. There is some indication of a 
rise in frequency with range, but the systematic rise 
is often obscured by the larger irregular changes. Of 
16 reverberations treated in this way, 10 showed 
sufficient systematic increase in pitch to be noted; if 


98 


ECHOES, SCATTERING AND REVERBERATION 


TIME, SECONDS 
2 0 I 2 0 I 2 0 


2 0 


810 


» J 

cn < 
a > 
o a: 

uj 

u 2 

ii 800 

So 

k a 

<o 

u -L 790 
x tr 

Id u 
> > 


< o 


780 


fW 


171 
















Figure 19. Graphs of reverberation frequency as a function of range. Average frequencies over 0.1-sec intervals 
computed from periodmeter records. 


there was such an increase in the other six, it was 
obscured by the irregular changes. In no case did the 
increase exceed 10 cycles in 2 sec (1,600 yd). 

While the periodmeter records are very useful for 
obtaining qualitative information about the modula- 
tion and distortion of reverberation and echoes, their 
quantitative evaluation is both laborious and un- 
certain. Slight modifications in the equipment would 
simplify the work. This would seem to be a fruitful 
field for further experimental and theoretical re- 
search. 

5.3.8 Reverberation from Chirps 

It has been suggested, for various reasons, that it 
might be advantageous to use modulated signals in 
echo ranging, rather than the constant frequency 
pings. If the frequency of the sound is increased 
during the transmission of the signal, it will sound 
like “chirp” rather than “ping”. The chirp is the 
form of modulation most often used. If the frequency 
increases from/ c at the beginning of the transmission 
to / +s at the end, the quantity s is called the sweep 
of the chirp. While a constant frequency ping is 
characterized only by its duration t 0 (or ping length 
r 0 ), a chirp is characterized both by its sweep and its 
duration. 

If the product st 0 is less than unity, the chirp will 
differ only slightly from the ping in most respects. 


Only if the product st 0 is much greater than unity 
will there be much difference. Thus a 1-msec ping 
and a 1-msec chirp with a sweep of 1,000 c will not 
differ greatly, but a 50-msec ping and a 50-msec 
chirp with a 1,000-c sweep will differ markedly. 

Theoretical analysis has established three general 
conclusions that are valid when st Q > 1. 

1. The average intensity of the reverberation from 
a chirp is the same as that from a ping of the same 
duration. 

2. The fluctuation or blob length of the reverbera- 
tion from a chirp is the same as that for a ping of 
duration 1/s. 

3. The duration of the echo from a concentrated 
target is approximately the duration of the chirp. 

These theoretical conclusions have not been very 
carefully checked by experiment, but they seem to 
be correct, as is illustrated by Figure 20. The oscillo- 
gram A shows reverberation from a 40-yd ping, and C 
that from a 0.8-yd ping. The oscillogram B shows 
reverberation from a 40-yd chirp whose sweep was 
1,000 c. It is seen that the intensity of the chirp 
reverberation is comparable to that of the 40-yd ping, 
while the duration of the blobs of the chirp rever- 
beration is comparable to that of the 0.8-yd ping. 
The echo shown on all three oscillograms is from the 
same target and is in accord with the third con- 
clusion. 

Several applications of these principles have been 
suggested, but further research is needed. 


REVERBERATION IN DEEP WATER 


99 



c 


Figure 20. Oscillograms showing effect of pulse length 
and modulation upon reverberation. (A) Forty-yard 
ping; (B) 40-yd chirp having 1-kc sweep; (C) 0.8-yd 
ping. 

5.4 REVERBERATION IN DEEP WATER 

5 . 4.1 General Remarks 

The experimental study of reverberation as a func- 
tion of range is greatly facilitated by the proper 
choice of two parameters : water depth and beam tilt. 
Thus, by observing reverberation from horizontal 
beams in deep water, it is usually possible to elimi- 
nate the effect of bottom reflections so that the ocean 


may be treated as a semi-infinite medium bounded 
by the surface. This allows comparison of the experi- 
mental results with the theory developed in Section 
5.3. 

In the study of volume reverberation a further 
simplification is gained by tilting the sound beam 
downward at a large angle, thus eliminating surface 
reflection and surface reverberation. The results of 
such tilted beam experiments are described in Sec- 
tion 5.4.2. 

With the beam directed horizontally the observed 
reverberation is a combination of both surface and 
volume reverberation. Moreover, both beam pattern 
and refraction effects are important. All these factors 
make the interpretation of these data more difficult. 
The results of such experiments are discussed in 
Section 5.4.3. 

Finally, in Section 5.4.5, a brief discussion will be 
given of forward scattering from the same volume 
scatterers which are responsible for volume rever- 
beration, or backward scattering. 

With the exception of the discussion of the de- 
pendence of volume reverberation on frequency, all 
the data described in this section were taken at 24 kc. 
It is also important to note that the data and the 
conclusions drawn therefrom are representative of 
the oceanographic conditions within a few hundred 
miles of the coast of California and Lower California. 
Since no deep-water reverberation data are available 
from other geographical regions, it is impossible to 
estimate the validity of these conclusions for oceanic 
waters in general. 

5.4.2 Volume Reverberation with a 
Tilted Beam 

The primary objective in using a tilted beam is the 
elimination of surface reverberation. To achieve this, 
it is necessary to employ a highly directional beam 
tilted at a dip angle of 30 degrees or more below the 
horizontal. This procedure also eliminates two other 
complicating factors: surface reflection and refrac- 
tion, and the transmission anomaly is thus determined 
entirely by losses due to absorption and scattering. 
Neglecting the attenuation loss due to absorption and 
scattering, the transmission is therefore inverse square. 

Dependence of Volume Reverberation on Range 

It will be recalled (Section 5.3) that if the volume 
scatterers are uniformly distributed and the trans- 


100 


ECHOES, SCATTERING AND REVERBERATION 


mission is inverse square, the intensity of volume 
reverberation decreases as the square of the range 
(or, with a vertical beam, the depth). Thus the theo- 
retical reverberation level (equation 28) decreases 
20 db per tenfold increase in range. Figure 21 shows 
an example of this dependence. 10 The data were taken 


RANGE, YD 



Figure 21. Dependence of volume reverberation on 
range. The straight line represents an inverse square 
variation. Experimental data taken in 600-fathom 
water with the transducer tilted downward 60 degrees. 
The close fit is exceptional. 

in 600-fathom water with the transducer tilted down- 
ward 60 degrees. The observed points are seen to fit 
the theoretical solid line quite closely. 

Such good agreement between observed levels and 
equation (28) is not often experienced. Usually the 
reverberation graphs, while exhibiting an overall 
decrease with range more or less in conformity with 
the equation (28), have maxima and minima much 
more pronounced than those in Figure 21. This is il- 
lustrated in Figure 22, which is the graph of rever- 
beration measured in the same location as that of 



Figure 22. Volume reverberation measured under 
the same conditions as in Figure 21, five days later. 
The data shown here are more typical than those of 
Figure 21. 

Figure 21, five days later. It is seen that the spread 
between maximum and minimum values is as much 
as 10 db greater than in Figure 21. 


Deep Scattering Layers 

These departures from the theoretical variation of 
reverberation with range are ascribed to the fact that 
the scatterers in the ocean are not distributed uni- 


RANGE, YD 

0 1000 2000 3000 4000 



Figure 23. Reverberation from the deep scattering 
layer. The insert shows the geometry. The peak at A 
at a range of 400 yd is ascribed to scattering from this 
layer (marked A in the insert), the average depth of 
which was 300 yd. The peak at B is ascribed to bottom 
reverberation; the one at C may be due to sound 
traveling via PABCBAP or PABC'BAP. 

formly throughout the medium, as was assumed in 
deriving the equations ; rather, the shape of the curves 
implies that they occur in horizontal layers at various 
depths and in varying concentrations. 

There is ample experimental evidence for the ex- 
istence of such scattering layers at considerable 

DEPTH, YD 



Figure 24. Reverberation from the deep scattering 
layer, with the beam directed vertically downward. 
The peak at A is ascribed to this scattering; the one 
at B is sound reflected from the bottom. 

depths. Figures 23 and 24 are typical specimens of 
reverberation graphs from data taken in deep water 
with tilted beams. The data of Figure 23 were taken 
in water 1,300 yd deep; the transducer was tilted 


REVERBERATION IN DEEP WATER 


101 


1905 1915 


1920 


PACIFIC WAR TIME 
1930 1940 


^jgggSSgjj^ 

I L"im. -lir- 1 - t 


500- 


1950 


1955 







ASCENT OF ECR LAYER IN THE EVENING 
18 AUGUST, 1945, 18 KC 


•BOTTOM 


500- 


0610 


06 20 


0630 



BOTTOM 


n ■ ~ .... 


DESCENT OF ECR LAYER IN THE MORNING 
19 AUGUST 1945 S8 KC 


DIURNAL VARIATION OF REVERBERATION WITH VERTICAL BEAM 

Figure 25A. Diurnal variation of the deep scattering (ECR) layer. 


, 


downward 49 degrees. The sharp peak (A) at a range 
of about 400 yd is ascribed to scattering from a layer 
at a depth of about 300 yd, in which the scatterers 
are more numerous than in the neighboring water; 
from the width of the peak the layer appears to be 
about 100 yd thick. The insert shows the geometry. 
The large peak ( B ) at 1,800-yd range is reverbera- 
tion from the bottom; the third peak (C) at 3,000 yd 
is probably due to sound scattered from the bottom a 
second time, after the first bottom-scattered sound 
was reflected to the surface and thence scattered back 
to the bottom — sound that traveled the path 
PABCBAP, or to the scattering layer and back, via 
PABC'BAP. 

The data of Figure 24 were taken at the same time, 
the beam in this case being directed vertically down- 
ward. The presence of the deep scattering layer at 
300 yd is again evident (A). The sharp peak (B) is 
due to sound reflected from the bottom at normal 
incidence. 

The presence of the deep layer off the southern 
California coast was first discovered in the summer of 


1942 in the course of experiments of the type described 
above. It was found that in a given area the same 
deep scattering layer tended to persist for periods of a 
month or more, although it occasionally became dif- 
fuse, with the result that the sharp peak in the rever- 
beration curve disappeared. Subsequent studies using 
a vertically directed beam, were made off Lower 
California during cruises of the USS Jasper to Guada- 
lupe Island in 1943 and to La Paz in 1945, as well as 
in the San Diego area and as far north as San Fran- 
cisco. These experiments indicate that throughout 
the year such layers are common from as far north as 
San Francisco to as far south as Cape San Lucas, and 
extend 400 miles out to sea from the California 
coast. In many cases two or more distinct layers were 
detected at various depths. 

These investigations have shown that the deep 
scattering layer undergoes a diurnal cycle (see Figure 
25 A) . This is shown schematically in Figure 25B and 
may be described as follows : 

1. During the day the layer is more or less con- 
centrated at one depth, 300 yd being typical. 




102 


ECHOES, SCATTERING AND REVERBERATION 


TIME 


NOON MIDNIGHT NOON 

SUNSET SUNRISE 



Figure 25B. Diurnal variation of the deep scattering 

(ECR) layer. 

2. In the late afternoon and early evening the 
layer moves toward the surface. 

3. From midnight to sunrise some of the scatterers 
move downward and the layer becomes diffuse, with 
the scatterers distributed between the surface and a 
depth of 200 or 300 yd. 

4. Finally, from sunrise to midmorning the re- 
maining scatterers near the surface move downward 
and the layer again becomes concentrated. 

These facts suggest the occurrence of scatterers 
that migrate with a daily schedule. Their nature has 
not been definitely established. However, biological 
studies have shown that plankton (the passively 
floating or weakly swimming organic life found in 
bodies of water) executes a diurnal migration cycle, 
going to depths of at least 200 yd. It appears reasona- 
ble to conclude that these scattering layers may be 
colonies of plankton, or fish feeding on it, or possibly 
bubbles generated by it. a 


The Determination of the Volume-Scattering 
Coefficient 

It is possible to calculate the volume-scattering 
coefficient m by comparing observed and theoretical 
reverberation levels. The most suitable data for this 
purpose are those taken with a vertically directed 
beam and a short ping length, such as those shown in 
Figure 24. There are two reasons for this. First, the 
geometry is such that at each range the scatterers are 
essentially uniformly distributed within the active 
volume, as assumed in the theory developed in 

a It has been suggested that this layer be called the “ECR 
layer.” “ECR” was the designation of the research group 
that discovered and studied it as well as the initials of the 
three leaders of the group, C. F. Eyring, R. J. Christensen, 
and R. W. Raitt. 


Section 3. Second, the transmission loss is the same 
for all scatterers and is given by 

H v = 20 log r + ar. (33) 

The first term, 20 log r. is the inverse square loss, r 
in this case being the depth; the second, ar, takes 
account of losses by absorption amounting to a db/yd. 
Using this value of H in equation (30) the volume 
reverberation level becomes 

RL V — /„+ 10 log mr 0 — 20 log r — 2 ar. (34) 
This equation contains seven variables: of these, 
J v , r 0 , r, and RL 0 can be determined quite accurately 
by measurement. The value of a appropriate to 
vertical transmission is not accurately known (see 
Chapter 3). The error inherent in this estimate is 
serious only for large values of r (great depths) and 
for high frequencies. 

The scattering coefficient m can then be calculated 
from equation (34). An example using the reverbera- 
tion levels plotted in Figure 24 is shown in Figure 26. 
In this example r 0 = 8 yd, J v = — 25 db, and a is esti- 
mated to be equal to 0.0045 db/yd. It is seen that the 


io log m,DB 



Figure 26. Volume-scattering coefficient, 24-kc. 


value of 10 log m ranges from a maximum of — 53 db 
in the ECR layer to a minimum value of — 85 db at a 
depth of 700 yd. The values of m corresponding to 
these are respectively 


m = 5X 10 -6 yd -1 , 
m = 3 X 10~ 9 yd -1 . 


and 


REVERBERATION IN DEEP WATER 


103 


They are typical of the maximum and minimum 
values commonly observed. Values as low as 10 -10 
have been observed. The minimum values that can 
be measured are determined by the level of the back- 
ground noise in the receiver. It is probable that with 
lower noise levels even smaller values would be ob- 
tained on occasions. 

While it is difficult, because of the wide spread in 
the observed values, to give a single average value, 
the values summarized in Table 3 may be considered 
fairly representative. 


Table 3. Values of the surface scattering coefficient 
n at 100-yd ranges. 


Wind speed 

10 log n 

n 

8 (mph) 

-54 (db) 

4 X 10~ 6 

10 

-45 

3 X 10~ 5 

15 

-33 

5 X 10-4 

20—40 

-24 

4 X 10-3 



10 log m, DB 
-80 -70 -80 -70 


-80 -70 -60 



Figure 27. Volume-scattering coefficient at various 
frequencies. 


ured reverberation levels, using equation (34). The 
values of the attenuation coefficient a, based on 
available data on attenuation of sound in the sea, 12 
are as follows: 


Scattering Does Not Cause Appreciable At- 
tenuation 

It has been remarked that scattering is theoreti- 
cally responsible for some attenuation. These numeri- 
cal results can be used to estimate the importance of 
this cause of attenuation. If scattering were the only 
cause, the attenuation of 20-kc sound in the ECR 
layer would be only about one-tenth that due to vis- 
cosity and much less than 1 per cent of that actually 
observed. In regions of smaller scattering coefficient, 
and for higher frequencies, these ratios are even 
smaller. It may therefore be concluded that scatter- 
ing is not a cause of the anomalously high-attenua- 
tion coefficients (see Chapter 3). 

Dependence of Volume Reverberation on 
Frequency 

The discussion of volume reverberation has thus 
far been limited to data taken at 24 kc. During Janu- 
ary and February 1943, an extensive series of meas- 
urements was made with vertical beams at four other 
frequencies: 10, 20, 40, and 80 kc. The observations 
were made at nine stations between San Diego and 
Guadalupe Island, about 250 miles south. The ocean 
depth varied from 600 to 2,000 fathoms. 

The ECR layer was observed at all positions and 
at all four frequencies. Figure 27 shows the average 
scattering coefficient at each frequency as a function 
of depth. The curves were obtained from the meas- 


Frequency (kc) a (db per yard) 

10 0.00135 

20 0.0036 

40 0.0097 

80 0.024 

The four curves are seen to be very similar, with 
comparable values of m both near the surface and at 
the depth of maximum scattering (about 450 yd). 
Below this depth the 10-kc and 20-kc curves are 
similar but the 40- and 80-kc curves do not show a 
decrease in the value of m; this is probably only ap- 
parent, and may be the result of experimental errors 
caused by higher noise levels at these frequencies. It 
is probable that had the noise levels been lower at 
the two higher frequencies, the observed values of 10 
log m would have decreased again below the 450-yd 
depth. 

A comparison of m at the four frequencies is made 
in Figure 28. Curve 1 represents average values in 
the upper 250 ft of the ocean (indicated by arrows in 
Figure 27). These values are essentially independent 
of the values assumed for the attenuation, since even 
at 80 kc the term 2 ar in equation (34) is less than 5 
db. The values of 10 log m show an increase with 
frequency which is only slightly greater than the ex- 
perimental error and is considerably less than the 
irregular variations at a single frequency. Thus m 
may vary as the first power of the frequency or, at 
most, as the second power. It is decidedly less than 
that of curve 3, which shows the Rayleigh fourth- 


104 


ECHOES, SCATTERING AND REVERBERATION 


-40 


-50 


6 - 70 
l -00 

- -90 
-100 


1— DEPTH 80 YD 

2 — DEPTH 450 YD 

3— RAYLEIGH LAW 












3 . 









2 


“3 

y- 


> — < 

> ^ / 

4 

) 

> 

, 


( 

r* 










FREQUENCY, KC 


Figure 28. Comparison of volume-scattering coeffi- 
cients at different depths with the theoretical Ray- 
leigh scattering. The data are those of Figure 27. 


power variation (Section 5.2.2) predicted for small 
solid or liquid particles having dimensions less than 
the wavelength of the sound. 


experimental evidence cited there is conclusive that 
the second cause is the dominant one. These calcu- 
lations indicate that the first cause should be domi- 
nant and that the fluctuations of reverberation in- 
tensity should be much greater than is actually 
observed. 

These calculations have been based on the assump- 
tion that the scatterers are solid particles or liquid 
droplets. If they should be gaseous bubbles, Figure 1 
shows that their actual diameters might be much less 
than the value deduced above. However, the effective 
target areas of the resonant bubbles are so much 
greater than the actual cross section that the argu- 
ment is not greatly changed, and the paradox remains 
for all except the longest pings. 

It is worth noting that the paradox is a contra- 
diction between two theoretical conclusions, drawn 
from different experimental data. Its resolution will 
therefore require theoretical as well as experimental 
research. 


A Paradox Concerning Reverberation 

These results are very difficult to reconcile with 
other facts concerning reverberation. This may be 
illustrated by a simple calculation. The lack of de- 
pendence on frequency may be explained if the scat- 
terers have diameters greater than one wavelength 
of 10-kc sound, i.e., d ^ 0.16 yd. For these, Figure 1 
shows that their target areas will be constant (to 
within 5 db) for all higher frequencies. The target 
areas of each scatterer will then be o = J ^wd 2 , or o^ 0.02 
yd 2 . Since the scattering coefficient is approximately 
m = No , where N is the number of scatterers per 
cubic yard, we can estimate N. If m = 10 ~ 6 yd -1 , it 
follows that N ^ 5 X 10 -5 yd~ 3 , if ra= 10~ 8 , then 
N ^ 5X 10~ 7 yd. That is, there will be about one 
scatterer per million cubic yards of water. 

This may be compared to the active volume of a 
ping at 250 yd from the projector. The width of the 
beam is involved in this calculation; supposing it 
to be 6 degrees, the active volume is 2,000 r 0 yd 3 , r 0 
being the ping length. Taking r 0 = 50 yd, it follows 
that the active volume is 10 5 yd 3 . In general, 
therefore, there should be no scatterer in the active 
volume. Only once in every two or three transmis- 
sions would there be any reverberation at the 
given range of 250 yd; on this one occasion, the 
intensity would be several times that which is actu- 
ally observed. 

To put the matter in another way, two causes for 
the fluctuation were suggested in Section 5.3.5. The 


5.4.3 Volume and Surface Reverberation - 
with a Horizontally Directed Beam 

When the transducer is directed horizontally in 
deep water, both surface and volume reverberation 
are generally observed. The intensity of the resulting 
reverberation at each range will therefore depend on 
which of these two types of reverberation is domi- 
nant. Thus, as will be shown below, volume reverbera- 
tion is always dominant at long ranges, while at short 
ranges surface reverberation usually dominates. 

It is convenient to begin the discussion with aver- 
age reverberation-range curves obtained under prac- 
tical echo-ranging conditions. Surface and volume 
reverberation will then be considered separately in 
more detail; finally, average values of the scattering 
coefficients will be given. 

Average Reverberation Curves 

Two reverberation curves are shown in Figure 
29 A; they are averages of an extensive set of ob- 
served reverberations at high and low wind speeds. 
About 110 reverberation curves were obtained, each 
being an average of five successive pings. The spread 
of the individual points about each of the two average 
curves was very small, the quartile deviation being 
only about ± 5 db. The measurements were made at 
24 kc, using echo-ranging equipment with the trans- 


REVERBERATION IN DEEP WATER 


105 


RANGE, YD 



Figure 29A. Effect of wind speed on average rever- 
beration level. 


ducer mounted at a depth of 16 ft. Ping lengths of 
16 to 80 yd were employed but the reverberation 
levels were all corrected to a standard ping length 
of 80 yd. 

The two curves exhibit the following features: 

1. At short ranges (less than 500 yd) the average 
reverberation level depends strongly on the rough- 
ness of the sea surface as measured by wind speed. 

2. At long ranges (beyond 1,000 yd) the average 
reverberation is independent of wind speed. 

RANGE, YD 


0 1000 2000 3000 4000 



Figure 29B. Same data plotted on linear range scale. 


3. With high wind speed the reverberation level 
drops rapidly, the slope of the average curve (curve 
1) indicating a dependence on range as about r -5 . 

4. With low wind speeds the reverberation drops 
more slowly, the average slope (curve 2) between 
100 and 1,000 yd being roughly inverse square. 

The curves are also shown in Figure 29B on a 
linear range scale. 

The dependence of the short-range reverberation 
on wind speed clearly indicates that at ranges shorter 
than 500 yd and at high wind speeds, surface rever- 
beration completely dominates volume reverberation. 


This conclusion is supported by observations made 
at nearly the same time with horizontal and vertical 
beams. At high wind speeds it is found that at short 
ranges the reverberation levels obtained with a hori- 
zontal beam are much higher than those obtained 
with a tilted beam. Figure 30 shows data of this type 
taken at a wind speed of 17 mph. Comparison of the 
two curves shows that in the first 100 yd the 
horizontal reverberation is about 20 db above the 
vertical reverberation. Two scattering layers ( A 
and B) are also shown in Figure 30 at depths of 80 
and 400 yd. 


RANGE, YD 

O 200 400 600 800 1000 



Figure 30. Comparison of reverberation at wind speed 
of 17 mph with horizontal and vertical beam. Points 
A and B represent deep scattering layers. 


At low wind speeds (curve 2 of Figure 29A) the 
short-range reverberation is volume reverberation. 
The evidence for this statement is afforded by experi- 
ments of the type described in the previous paragraph. 
When such measurements are made at very low wind 
speeds, with the sea dead calm, it is found that the 
horizontal reverberation is much lower than in 
Figure 30 and agrees well with the vertical reverbera- 
tion. From this it is concluded that at very low wind 
speeds volume reverberation is dominant and surface 
reverberation is negligible. 

Finally, at long ranges, Figure 29A shows the 
reverberation to be independent of wind speed. This 
is taken as evidence that at these ranges volume 
reverberation always dominates surface reverbera- 
tion. 

Thus three main conclusions may be drawn re- 
garding deep-water reverberation with a horizontal 
beam. 

1. At short ranges and high wind speeds, surface 
reverberation is high and dominates volume rever- 
beration (curve 1, Figure 29). 




ECHOES, SCATTERING AND REVERBERATION 


106 



Figure 31. Comparison of observed and calculated 
surface reverberation. (A) Measurements made with 
transducer that was almost nondirectional in the 
vertical plane. Horizontal beam. (B) Data taken the 
same day under similar conditions, but with transducer 
turned so its directionality in the vertical plane was 
high. The theoretical curve takes account of the beam 
pattern. 

2. At short ranges and low wind speeds surface 
reverberation is negligible and volume reverberation 
is dominant (curve 2, Figure 29). 

3. At long ranges (beyond 1,000 yd) volume rever- 
beration dominates at all wind speeds and is inde- 
pendent of wind speed. 

Surface and volume reverberation will now be con- 
sidered in more detail. 

Surface Reverberation 

The discussion of surface reverberation given in 
Section 5.3 predicts an inverse third-power depend- 
ence on range. An example of this is shown in Figure 
31A. The data were taken with a transducer almost 
nondirectional in the vertical plane and mounted at 
a depth of 20 ft. Short pings, 6.4 yd long, were used. 
Wind speed was about 15 mph, so that the resulting 
reverberation can be identified as surface reverbera- 
tion. It is seen that the observed points agree well 
with the theoretical inverse cube law. 

Figure 3 IB is a reverberation curve taken the same 
day under similar conditions. In this case, however, 
the transducer had a pattern in the vertical plane 


which was highly directional (the axis of the beam 
was horizontal in both cases). At very short ranges 
the active surface area is insonified by the outer 
portions of the beam, beyond the angle a; these por- 
tions emit sound of a lower intensity than the main 
beam, and the receiver has a lower response at large 
angles than on the axis; thus there occurs a notice- 
able drop in the reverberation level. This can be 
calculated from the beam pattern as is shown by 
the solid curve. At ranges greater than 80 yd the 
active area is insonified by the main beam only, and 
the measured reverberation levels are seen to fit the 
inverse third-power line closely. 

The curves in Figure 31 must not be regarded as 
universal. Examples of reverberation curves that 
show an inverse fifth-power variation of the reverber- 
ation with range are frequent. (Curve 1 of Figure 29 
is an example.) The reason for this rapid decay is 
not understood. 10 

One case in which the surface reverberation is 
frequently observed to drop off more rapidly than 

TEMPERATURE F RANGE, YD 

50 60 70 O 500 1000 


m RANGE, YD 



Figure 32. Effect of downward refraction on rever- 
beration. (A) Bathythermogram and corresponding ray 
diagram. (B) Comparison of observed results with 
those calculated from simple theory. A sharp drop in 
the reverberation level at the arrow correspond^ to 
the range at which the sound beam leaves the surface. 

the inverse cube can be explained. Under conditions 
of strong downward refraction the reverberation 
would be expected to decrease at that range where 
the sound beam is bent away from the layer of sur- 





REVERBERATION IN DEEP WATER 


107 


face scatterers. Figure 32B shows an example of 
this drop, indicated by the arrow. It occurs at about 
300 yd; at greater ranges the reverberation level is 
some 20 db below the value as given by equation 
(29). The data were taken with short (9-yd) pings. 
The transducer depth was 20 ft and the wind speed 
12 mph. From the ray diagram based on the bathy- 
thermogram shown in Figure 32A, it is seen that the 
limiting ray leaves the surface at about 300-yd range 
(indicated by an arrow), thus affording support for 
the explanation suggested above. 

The dependence of surface reverberation on wind 
speed is very marked at short ranges, as can be 
seen in Figure 29: at 100 yd the reverberation level 
at high wind speeds is some 35 db above that for 
low speeds, but at 500 yd the difference is only 10 
db. The rapid increase of reverberation at 100 yd 
is seen more clearly in Figure 33 in which the 
average reverberation level is plotted against wind 
speed. The quartile deviation of the individual 
points about the smooth curve of Figure 33 is 
about ± 5 db. 


WIND SPEED, MPH 

O 10 20 30 40 



Figure 33. Dependence of reverberation level at short 
range (100 yd) on wind speed. 


It is seen that the reverberation level is constant 
for wind speeds up to 8 mph. This confirms the 
conclusion that volume reverberation is dominant 
at these low wind speeds. For wind speeds of 8 to 
20 mph the reverberation increases 35 db ; the curve 
then levels off and above 20 mph there is little 
further dependence on wind speed. This dependence 
on wind speed is closely correlated with the rough- 
ness of the sea. At 8 mph the wind is strong enough 
to roughen the surface appreciably; occasionally 
wavelets may slough over, but no well-developed 
whitecaps are observed. At about 10 mph small 
whitecaps begin to appear, and when the wind has 
reached 20 mph the sea is liberally covered with 


them. When this stage is reached, further increase 
in whitecaps has no effect on the reverberation. 

Correlation of reverberation with other measures 
of surface roughness (sea state, wind force, and 
swell) show similar results. In all cases, the rever- 
beration level shows a marked dependence at short 
ranges and negligible dependence at long ranges. 

Surface Scattering Coefficient 

It has been pointed out that surface reverberation 
in the ocean rarely exhibits the inverse third-power 
dependence on range which is predicted by the 
simple theory. This lack of agreement is found even 
at short ranges (100 to 500 yd), as shown by the 
steep slope of curve A in Figure 29. Thus it is clear 
that even the average surface reverberation cannot 
be fitted by equation (29) at all ranges. It is possible, 
however, to apply the equation to the observed 
reverberation level at one range to obtain the scat- 
tering coefficient as a function of wind speed. Table 3 
shows values of n obtained in this way from the 
observed levels at 100 yd (Figure 33) . 

Values oi J s = — 15 db and r 0 = 80 yd were used, 
corresponding to standard gear using 80-yd pings 
at 24 kc. Since the projector was at a depth of 16 
ft, these values correspond to an incident grazing 
angle at the surface of about 3 degrees. 

Volume Reverberation 

The simple theory of volume reverberation de- 
veloped in Section 5.3 assuming inverse square 
transmission and uniform distribution of volume 
scatterers predicts an inverse square dependence on 
the range. The first assumption is approximately 
valid at short ranges but breaks down at long ranges 
because of refraction and attenuation effects. The 
second assumption is sometimes valid over a limited 
region; in general, however, the horizontal stratifi- 
cation of the scatterers (Section 5.4.2) invalidates 
the assumption that they are uniformly distributed. 
Thus it is clear that the two basic assumptions made 
in the simple theory are usually not satisfied. 

In order to take account of refraction and the 
uneven distribution of scatterers, it would be neces- 
sary to carry out a volume integration over the 
active scattering volume at each range. There is 
insufficient data to warrant such a complex theory. 
The correction for attenuation, however, is easily 
made [equation (34) ] and has already been discussed 


108 


ECHOES, SCATTERING AND REVERBERATION 


in Section 5.4.2, in connection with the calculation 
of the volume scattering coefficients. Finally, it can 
be shown that surface reflection will, on the average, 
raise the reverberation given by equation (34) by 
an additional 3 db. Thus, for a horizontal beam, 
the theoretical volume reverberation, corrected for 
surface reflection and attenuation, is given by 

RL V = J v + 10 log mr 0 — 20 log r — 2 ar + 3. (35) 

The observed volume reverberation beyond 1,000 
yd agrees very closely with the theoretical reverber- 
ation given by equation (35) for typical values of a 
and m. This is shown in Figure 34. Curves 1 and 2 
are the observed averages at high and low wind 
speeds shown in Figure 21 and are repeated here for 
convenience. Curves 3 and 4 were calculated from 
equation (35) using attenuation coefficients of a = 0 


RANGE, YD 



2 

i 

S 

1 

t I 

> : 

1 

2 


s 






^ 1 

s 












> 












T 



'V 



^3 









N 

\ 


' 

OBSERVED REVERBERATION 

fl-WIND SPEED 20 MPH 

12-WIND SPEED ± 8 M PH 

THEORETICAL VOLUME 
REVERBERATION 
(3— WITHOUT ATTENUATION 

U-WITH ATTENUATION 


\ 

\ 




V 



A 


Figure 34. Comparison of calculated and observed 
volume reverberation, showing the close agreement. 


and a = 0.0045 db/yd, the latter typical of good 
transmission at 24 kc. For the remaining parameters 
the following values were used : 

J v = -25 db, 

7*0 =80 yd, 
m = 10~ 6 yd -1 . 

The value of m is the average value given in Table 
3 for the deep scattering layer. 

The importance of attenuation at long ranges is 
strikingly shown by the large differences between 
curves 3 and 4. Thus, at 5,000 yd the attenuation 
reduces the reverberation level by some 45 db be- 
low the inverse square value of curve 3. It should 
also be noted that the shape of the theoretical 
curve 4 beyond 1,000 yd is determined largely by 
the particular value of the attenuation coefficient a. 


To return to the fit between equation (35) and 
the average curve at long ranges: not only does 
curve 4 fit the average volume reverberation, but 
it also gives a fair fit to most individual reverbera- 
tion curves. This is shown by the small spread of 
the individual points around the average curve, 
half of the points lying within + 5 db of the average. 
These results indicate that the long-range volume 
reverberation is due largely to the ECR layer. 
Further evidence for this conclusion is afforded by 
the fact that at short ranges, where the sound beam 
has not yet reached the ECR layer, the observed 
volume reverberation (curve 2) falls below the 
theoretical curve. 

It has been remarked that beyond 1,000 yd most 
individual reverberation curves fit curve 4 quite 
closely. This is true over a wide range of oceano- 
graphic conditions, with one exception: no signifi- 
cant dependence has been found on wind speed, sea 
state, location, season, or thermal structure of the 
ocean. 

The exception occurs under conditions of extremely 
sharp downward refraction and provides an interest- 
ing check on the importance of the ECR layer. 

The effect of sharp downward refraction is to 
concentrate the sound beam into a relatively nar- 
row cone. This produces a maximum in the rever- 
beration curve at the range where the sound beam 
reaches the layer. An example of this effect is shown 
in Figure 35, where refraction and reverberation 
are compared for two days. The data were taken 
late in the afternoon off La Paz, using standard 
gear and 80-yd pings. 

On the first day there was a deep mixed layer 
extending from the surface to a depth of 40 yd. 
Figure 35A shows the ray diagram and the deep 
scattering layer. The angle shown on each ray is 
the angle of the ray at the projector, measured down- 
ward from the horizontal; the 6-degree ray is the 
effective lower edge of the sound beam. Two days 
later, on March 17, the same deep layer was still 
present, but thermal conditions had changed rad- 
ically, producing the strong downward refraction 
shown in Figure 35B. (The dotted rays 1 and 2 
will be discussed later in connection with forward 
scattering.) 

Typical reverberation curves for each day are 
shown in Figure 35C together with the theoretical 
reverberation (curve 4) of Figure 34. It is seen that 
the reverberation observed when there was a mixed 
layer (curve 1) agrees well with the theoretical 


REVERBERATION IN DEEP WATER 


109 


range, yds 




Figure 35. Comparison of reverberation and refrac- 
tion for two days. (Top) Ray diagram for March 15, 
1945. The shaded portion indicates the ECR layer. 
(Center) Ray diagram for March 17, 1945. (Bottom) 
Observed reverberation for these two days compared 
with calculated values. 

curve 3 between 1,000 yd and 2,500 yd; beyond 
2,500 yd it reaches the noise level and flattens out. 
Curve 2, on the other hand, observed when there 
was sharp downward refraction, shows a large 
maximum at about 2,000 yd, corresponding to the 
range at which the central portion of the sound 
beam reached the depth of maximum scattering 
(Figure 35B). 

At short ranges, curve 1 rises steeply with decreas- 
ing range. This rise is due to surface reverberation 
and is to be expected, since the data were taken at 
a wind speed of 20 mph. The data of curve 2 were 
taken at a wind speed of 12 mph; it shows a cor- 
responding rise in the reverberation level at very 


short ranges (100 yd), but there is a minimum when 
the sound beam has left the surface and has not yet 
reached the scattering layer. When the lower edge 
of the beam reaches the deep layer (about 1,000 
yd) the reverberation begins to increase with in- 
creasing range, culminating in the main maximum. 

544 Bottom Reverberation 

Since in echo ranging the transducer is generally 
near the surface, the sound scattered back from the 
sea bottom will provide an important contribution 
to the reverberation only in shallow water; here, 
however, it may well be the dominant factor in 
limiting the range from which detectible echoes can 
be obtained. 

Types of Sea Bottom 

In the case of surface reverberation, it is the state 
of the sea that determines the intensity of the scat- 
tered sound; bottom reverberation levels, it may be 
expected, will depend on the character of the sea 
bed. In practical work four types of bottom are 
recognized — Rock , Sand, Mud and Sand, and Mud. 
The criterion of classification is the size of the part- 
icles constituting the sea bed, as determined by 
examining samples obtained by sounding with special 
devices. Recently, also, techniques of underwater 
photography have been perfected and have proved 
useful in studying the bottom. The difference in 
reverberation intensities among these various bot- 
tom types will be discussed below in connection 
with the discussion of bottom scattering coefficients. 

Transmission Loss — Surface Reflection 

It is obvious, from the discussion of Figure 5 in 
Section 5.3.3, that any bottom reverberation that 
occurs will be combined with volume reverberation, 
and, when a horizontally directed beam is used, 
with surface reverberation. Thus we can not expect 
that the measured levels of what is, from the geom- 
etry of the experiment, predominantly bottom re- 
verberation, will necessarily have the levels predicted 
by the simple theory expressed by equation (31). 
(It will be recalled that equation (31) applies to 
bottom reverberation as well as to surface reverbera- 
tion.) However, in shallow water over a bottom that 
scatters strongly, such as rock, the bottom reverbera- 





110 


ECHOES, SCATTERING AND REVERBERATION 


tion may be so much greater than either the surface 
or volume reverberation that a rough check of the 
theory is possible. In attempting this, however, the 
simple inverse square loss will not provide a very 
reliable guide to the transmission loss. One must 
consider also the loss due to attenuation. 


RANGE 



RANGE 



Figure 36. Schematic diagrams illustrating surface 
and bottom reverberation and comparing the cases of 
no refraction (A) and strong downward refraction (B). 


In addition, the effect of the surface in reflecting 
the sound incident on it toward the bottom, from 
which it may be scattered back to the transducer 
either directly or by way of the surface a second 
time, must be taken into account. Considering the 
surface to act as a perfect reflector, it is evident 
that, if refraction is neglected, the intensity of the 
direct sound at the bottom will be doubled, thus 
doubling the intensity of the scattered sound. More- 
over, the reflection of this scattered sound from the 
surface causes the intensity at the transducer to be 
doubled. Hence, the surface increases the intensity 
of the reverberation fourfold, or, expressed in dec- 
ibels, raises the reverberation level 6 db. 

These deviations from the inverse square loss can, 
in discussions, be conveniently combined with the 
latter in the term H s of equation (31). 


Effects of Refraction 

The effects of the refraction of the sound are more 
difficult to evaluate. The bending and distortion of 
the sound beam affects the intensity of the bottom 
reverberation in several ways. If the beam is bent 
sharply downward, the sound strikes the bottom at 



Figure 37. Data of an experiment illustrating the con- 
ditions shown in Figure 36. (A) Bathy thermogram; 

(B) ray diagram; (C) observed reverberation, curve 1, 
water depth 87 yd, curve 2, water depth 210 yd. 

a shorter range and may be more concentrated ; the 
surface reverberation will decay very rapidly, and 
the bottom reverberation may be more intense. This 
is illustrated schematically in Figure 36 A and B. It 
is clear from A that, if the beam is not refracted 
downward, surface reverberation will be received 
continuously after the beam first strikes the surface. 





REVERBERATION IN DEEP WATER 


111 


RANGE, YD 


0 1000 2000 3000 4000 



Figure 38. Comparison of calculated and observed 
reverberation in shallow water over mud bottom. 


On the other hand, as seen from B, a sharply re- 
fracted beam strikes the surface in a limited area 
only; thus the surface reverberation consists of a 
burst of sound that dies away very rapidly, to be 
followed by a second burst of sound as the bottom 
reverberation comes in. 

These effects are shown clearly in Figure 37. The 
bathythermogram shows the thermal pattern of the 
sea when the reverberation shown by curves 1 and 2 
in Figure 37B was measured. The two curves rep- 
resent reverberation in two different depths of water 
(87 and 210 yd, respectively) . The bending and distor- 
tion of the beam is seen in the ray diagram ; a dotted 
line showing the path of the — 6-degree ray in the 
absence of refraction is drawn in. The refracted 
— 6-degree ray strikes the bottom at ranges shorter 
by 500 and 1,200 yd at the two depths. Moreover, 
the beam is concentrated between the — 1 -degree 
and — 6-degree rays, but diverges strongly between 
the — 1-degree ray and the upper limiting ray. 
One would therefore expect the reverberation to 
decrease rapidly as soon as the upper half of the 
beam strikes the bottom, and both curves 1 and 
2 show this. The expected rapid decrease of the 
surface reverberation is also clearly shown. The 
difference in levels between the two curves is due 
to the difference in ranges to the bottom in the 
two cases. 

Comparison of Observed and Calculated 
Reverberation Levels 

A large number of bottom reverberation records 
have been plotted and compared with the graph 


RANGE, YD 



Figure 39. Like Figure 38, sand and mud bottom. 


of RL S as a function of r, as given by equation (31): 

( nr 0 \ 

— ) ~ 2 H s + 10 log r. (31) 

Of the terms in this equation, J s and r 0 are known ; 
the value of H s must either be predicted or else 
obtained by making transmission measurements as 
nearly siihultaneously with the reverberation runs 
as is practicable. The magnitude of the scattering 
coefficient n is, of course, not known, hence that 
value of n which will give the best fit with the ex- 
perimental points is considered to be the appropriate 
scattering coefficient. In determining the best fit, 
the region of the graph between 500 and 1,000 yd 
is given the greatest weight. 

The agreement between the calculated and observed 
reverberation is illustrated by Figures 38 to 41. Each 
of these exhibits results of measurements taken over 
a particular bottom type. Two theoretical curves 
are drawn for each bottom type except mud, in 
which case transmission data were available only for 
the case of poor transmission. The curves labeled 1 
represent good transmission conditions, those labeled 
2, poor transmission. The values of H s were measured 
in conjunction with the reverberation measurements. 

The experimental points represent averages of 
from 5 to 30 reverberation runs. The quartile de- 
viation is about ± 5 db on the average. All measure- 
ments were made using 80-yd pings. 

It should be stressed that these experimental data 
are not to be considered as representing bottom 
reverberation generally in shallow water. The meas- 
urements which yielded them were taken over 
particular small patches of particular bottom types. 


112 


ECHOES, SCATTERING AND REVERBERATION 


RANGE, YD 




Figure 40. Like Figure 38, sand bottom. 


Figure 41. Like Figure 38, rock bottom. 


The curves will serve, however, to convey a fairly 
realistic picture of the main features of reverberation 
in shallow water. 

The four figures have certain features in common. 
The fit in all cases is quite good for ranges less than 
1,500 yd. Beyond this range the measured reverbera- 
tion is consistently higher than the calculated; over 
mud bottom, the difference at 2,500 yd is 10 db; 
over sand and mud, it is 20 db at 2,000 yd. The 
reason for this divergence at longer ranges is not 
known. 


Bottom Scattering Coefficients 


Bottom type 10 log n 

Rock — 22 

Mud and Mud-Sand — 30 

Sand — 34 


The errors, systematic and random, may be as much 
as 5 db. 


5.4.5 Forward Scattering from 

the ECR Layer 

Simple refraction theory predicts a “black” shadow 
zone under conditions of strong downward refrac- 
tion. This is not confirmed by 24-kc transmission 
runs made in deep water off the southern California 
coast (see Chapter 3). Instead, sound of very low 
intensity is observed out to ranges of 5,000 yd 
(some 4,000 yd beyond the limit of the strong direct 
sound field), which can be explained neither as direct 
nor as bottom reflected sound. Instead, there appears 
good reason to believe that it is sound scattered in 
the forward direction from the ECR layer. 


Figure 42 illustrates this phenomenon diagram- 
matically. Two transmission curves are shown. The 
dotted curve indicates the level of the direct sound 
and is seen to drop rapidly with range. This drop 
occurs at roughly the range of the shadow boundary 
predicted by the ray diagram. The solid curve 
represents the level of the sound observed in the 
predicted shadow zone. It is seen that the trans- 
mission anomaly is of the order of 50 db and changes 
slowly with range. 

RANGE, YD 


O IOOO 2000 3000 4000 5000 



Figure 42. Diagram illustrating forward scattering. 
Transmission with strong downward refraction showing 
the signal form received at various ranges. 


The form of the signal as it is received at various 
ranges is illustrated schematically. At short ranges 
(A), well inside the direct sound field, only the strong 
direct signal is observed. In the region of the shadow 
boundary (B) the direct signal is much weaker and 
is followed by a “tail” which resembles reverbera- 
tion in appearance. The intensity of sound in the 
tail is shown by the solid curve. Finally, at ranges 
far beyond the shadow boundary (C), the direct 
signal has disappeared entirely and the reverbera- 




REVERBERATION IN DEEP WATER 


113 



Figure 43. Diagram showing forward scattering from 
the deep scattering layer. Sound scattered from each 
of the three scatterers A, B,C has a ping length (>*#**) 
equal to the ping length of the direct sound. Since the 
travel distances PAH, PBH, and PCH are nearly 
equal, the three pings of scattered sound are received 
in the forward direction almost -simultaneously at 
hydrophone H, thus constituting a pulse of scattered 
sound having a ping length equal to that of the direct 
sound. 

tion tail has contracted to a ragged pulse whose 
signal length is approximately that of the direct 
signal. If long signals are used, the intensity of the 
sound in the shadow zone is unchanged but the 
duration of the signal is correspondingly longer. 

Figure 43 shows schematically how forward scat- 
tering can explain the short pulse observed at long 
ranges. The explanation depends on the fact that 
the path differences, via the various scatterers, are 
small, so that all the scattered sound reaches the 
hydrophone at nearly the same time. With the hy- 
drophone at shorter ranges the path differences are 
larger and the scattered sound is received over a 
longer period. This “smears” out the pulse and 
explains the presence of the tail. 

The level of the scattered sound which this 
mechanism predicts depends on the projector output 
and beam pattern, the scattering coefficient and 
thickness of the deep layer, and the angle between 
the incident sound and the horizontal (Figure 43). 

A check of the theory is possible in a few cases 
where vertical-beam reverberation measurements 
were made in conjunction with transmission runs. 
From the vertical reverberation data the scattering 
coefficient and layer thickness can be found. These 
can then be used to predict the level of the forward 
scattering. One such experiment was performed on 
March 17, 1945, the second of the two days com- 
pared in the previous section, with the refraction 
conditions and deep layer as shown in Figure 35B. 
Figure 44 shows the observed and predicted scat- 
tering for this case. Beyond 3,000 yd the scattered 


RANGE , YD 


0 1000 2000 3000 4000 5000 



Figure 44. Comparison of observed and calculated 
scattering. In this experiment a 24-yd ping at 24 kc 
was projected into water 1,500 fathoms deep. 


sound is no longer a short pulse but is spread out, 
and the predicted level is too high. When the hydro- 
phone range is greater than 4,000 or 5,000 yd the 
observed level should drop rapidly because the 
scattered sound will be refracted downward (along 
rays 1 and 2 in Figure 35B) before it reaches the 
hydrophone. No observations are available at such 
long ranges to check this, however. 

The general good agreement between the theory 
and the observations, in the few cases which can be 
checked, indicates two main conclusions: 

1. Sound observed in the shadow zone under 
conditions of sharp downward refraction is forward 
scattering from the deep scattering layer. 

2. The scatterers in the deep scattering layer are 
approximately isotropic, i.e., scatter sound nearly 
equally in all directions. 

Appendix 

The reflection of sound by a large, perfectly reflecting 
sphere. Let the sound be incident in the direction 
QP, as shown in Figure 45. Consider the cap APB 
on the sphere which is cut out by a plane perpendicu- 
lar to the incident sound rays. It intercepts sound 
at the rate 

W = jw d 2 F sin 2 0 watts, (36) 

where F is the energy flow in watts per unit area at 
the target of the incident sound energy. All this 
energy is reflected, and since the angles of incidence 
and reflection are equal, all of it will be reflected in 
directions that make angles not greater than 2 0 with 
the incident beam. 



114 


ECHOES, SCATTERING AND REVERBERATION 



Figure 45. Diagram illustrating the calculation of the 
target strength of a sphere. 

Now consider a large sphere of radius r, concentric 
with the target. The reflected energy will pass through 


the cap CQD of the surface of this sphere. When r 
is much greater than d, and the angle 0 is not too 
large, the error involved in assuming that the points 
E and 0 are the same will be comparatively small. 
With this assumption the area of the cap is 

a = 2irr 2 (1 — cos 20) = 47rr 2 sin 2 0 (37) 

to a close approximation. It will be seen that, when 
0 is large, this estimate of the area involves neglect- 
ing the shadow FG of the sphere. On the other hand, 
when r is much greater than d, this shaded area FG 
is only a small fraction of the whole area of the 
sphere. Thus, the proportional error involved will 
be negligible. 

The average rate at which energy passes through 
the area CQD is given by 

W Fd 2 

— watts/yd 2 (38) 

a 16 r 2 

and since it is independent of the angle 0, it follows 
that it is also the rate at any point of the cap. 

Therefore, the energy is reflected (reradiated) 
equally in all directions, as stated in the text. 


Chapter 6 

WAKES 



Figure 1 . Wake of USS Moale (DD) at 20 ks from 2,500 ft. 


6.1 GENERAL DESCRIPTION 

6.1.1 Visual Appearance 

T he general nature of the wake of a ship is 
most readily seen from the air (Figures 1 to 4). 
The surface waves that spread out in a V behind 


the vessel and form a navigational hazard for 
near-by small craft are relatively inconspicuous 
from the air. Even the white bow wave, which 
breaks and sends foam back along the sides of 
vessel, is seen to be minor compared to the wake 
of turbulent, foamy water that fans out from the 
screws. 


115 


116 


WAKES 



Figure 2. USS Ringold (DD) from 300 ft. 







GENERAL DESCRIPTION 


117 




Figure 4. Swirl behind submarine after crash dive. 


Figure 3. Wake of surfaced submarine at 15 ks. 


This turbulent wake spreads rapidly for a fraction 
of the ship’s length, and thereafter widens only 
slightly (the divergence has been measured for var- 
ious wakes and found to vary from 0.5 to 5 degrees). 
The foam, which makes it visible from a distance, 
gradually disappears, but not until long after the 
ship has passed. The visual wake of a high-speed 
vessel extends twenty or even fifty ship-lengths astern. 

6.1.2 Other Properties of the Wakes of 
Surface Vessels 

It is fairly obvious that the violent disturbance 
which creates the turbulent wake will give it 
physical properties that differ to a greater or lesser 
extent from those of the undisturbed ocean sur- 
rounding it. 

Temperature Effects 

For example, if there is a temperature gradient 
in the upper part of the ocean, the mixing of the 
surface water with that of lower layers will give the 
water in the wake a different temperature from that 
of the nearby water at the same depth. This effect 


has been observed by the use of sensitive recording 
thermometers. The mixing of water from different 
depths may also result in anomalous density gra- 
dients. While these have not been investigated ex- 
perimentally, they may be important in causing the 
ultimate disappearance of the wake. 

Acoustic Properties of Wakes 

Of most interest from the present standpoint are 
the acoustic properties of the wake. They are prob- 
ably all associated with the presence of entrained 
air bubbles. The aerial photographs show that large 
numbers of bubbles remain in the wake for several 
minutes, and it is likely that some will remain sus- 
pended in the water even after the visible foam has 
disappeared. 

These acoustic properties of the wake are easily 
demonstrated with sonar gear. Figure 5 shows a 
record of echoes obtained from the wake of the 
E. W. Scripps. This vessel ran between the echo- 
ranging vessel and a small sphere, the echoes from 
the latter being recorded simultaneously with those 
from the wake. 

Two general conclusions can be drawn from Figure 
5. The wake echo gradually lengthens and becomes 



118 


WAKES 


Ul 

2 

H- 



WAKE 

ECHO 


SCREW NOISE 
E.W.SCRjPPS PASSING 


RANGE 


Figure 5. Range recorder trace of wake echoes from 
EW. Scripps . 


fainter, presumably because of the spreading of the 
turbulent wake and the gradual disappearance of 
the bubbles. Secondly, the sphere echo is weakened 


slightly, but noticeably, by the presence of the wake 
between the sonar and the sphere. 

In another experiment, a 40-ft motor launch, hav- 
ing a draft of only ft but with a wake extending 
to a depth of about 15 ft, passed between a standard 
24-kc sonar and a moored buoy. The echo from the 



Figure 6. Echo-sounding record from surface. Taken 
on submarine during a dive (photograph from USNEL, 
San Diego). 

buoy was reduced by 13 db after the passage of the 
launch and did not return to its original level for 
some 2 minutes. 

These conclusions are substantiated by a series of 
experiments performed by USNRSL (San Diego). 
An echo sounder was mounted in an inverted posi- 
tion on the deck of a submarine. When submerged, 
it was thus possible to echo range on the surface and 
record the depth of the submarine. This is illustrated 
by Figure 6, which is the record of a dive. The in- 
creasing depth during a dive is clearly indicated, as 
are the waves on the surface. 


THEORY OF THE ACOUSTIC PROPERTIES OF WAKES 


119 



Figure 7. Similar to Figure 6. Record made while submarine was passing under the wake of a surface vessel. (Photo- 
graph from USNEL, San Diego.) 


Figure 7 shows similar records made while the 
submarine passed under the wake of a surface vessel. 
In each of the two examples, it can be seen that the 
wake returned sound to the receiver, and also that 
it reduced the amount of sound returned from the 
surface. 

It may thus be concluded that the wakes of surface 
vessels have two major acoustic properties: they 
return echoes that are readily detectable by ordin- 
ary sonar gear, and they act as acoustic screens, 
reducing the intensity of the echoes from targets on 
their far side. 


6.2 THEORY OF THE ACOUSTIC 
PROPERTIES OF WAKES 

6.2.1 Air Bubbles As the Cause of 
Wake Echoes 

The two most obvious differences between a surface 
wake and the undisturbed ocean are its turbulence 
and its content of bubbles. It is therefore reasonable 
to assume that one or both of these are the cause 
of its acoustic properties. 


The possibility that turbulence is the cause of 
wake echoes is ruled out by theoretical considera- 
tions. It is true that when a sound wave passes 
through turbulent water it is scattered, but two 
facts exclude the assumption that this scattering is 
the cause of echoes. First, the scattering from tur- 
bulence is very weak unless there are great dif- 
ferences in velocity between pairs of points separated 
by one wavelength of the sound. Second, the inten- 
sity of the scattered sound depends strongly on the 
direction of scattering, and the intensity in the 
backward direction is zero. Thus, although turbulent 
water scatters sound, it does not return an echo. 

Turbulence might be an indirect cause of the 
echoes by mixing the warmer surface water with that 
from below. In this way, irregular differences of 
temperature are produced by the irregular differences 
in the turbulent velocity. Again, however, the mag- 
nitude of the expected effect is too small: in order 
to produce the observed echoes, temperature dif- 
ferences of nearly 1°F would have to occur between 
points only one wavelength apart. Such large tem- 
perature differences are very improbable. Moreover, 
if they were formed in some way, they would persist 
for a very long time, longer than wakes are observed 
to persist. 



120 


WAKES 


Thus, it may be concluded that the air bubbles in 
the wake are the major cause of the acoustic prop- 
erties of a wake. Several objections have been urged 
against this conclusion. One objection is based on 
the supposed short life of bubbles in water. Bubbles 
rise to the surface and break, so that they disappear 
from the wake in a short time; their disappearance 
is also hastened by solution of the air by the sea 
water. On the other hand, echoes have been obtained 
from wakes more than 10 minutes after the vessel 
passed, and there have been reports of echoes from 
wakes several hours old. The latter reports may be 
discounted, since it is very difficult to be certain of 
the position of a wake so long after the ship has 
passed, and it is quite possible that a school of fish, 
etc., might be mistaken for a wake under such cir- 
cumstances. It is therefore only necessary to show 
that some bubbles will remain suspended for periods 
of 10 to 30 minutes. 

Experimental evidence on this point was obtained 
by stirring the water of the pool at USNRSL with 
an outboard motor. The acoustic properties of the 
water were studied with an echo sounder. It was 
found that sound was returned from the body of the 



Figure 8. Rate of rise of air bubbles in still water: 
A. Rectilinear motion, spherical shape. B. Helical and 
twisting motion, flattened shape. C. Irregular. D. Rec- 
tilinear motion, distorted mushroom shape. 


water after stopping the motor. This return con- 
tinued even after all of the more obvious bubbles 
and turbulence had disappeared. Closer examination 
showed, however, that a relatively small number of 
small bubbles remained suspended. They were very 
difficult to see except when they drifted into a region 
of favorable illumination, so that neither their 
number nor their size could be accurately deter- 


mined. It was concluded that sufficient bubbles were 
present to explain the observed effects. This was 
based on the consideration that very small bubbles 
are quite effective in scattering sound but rise 
very slowly (see Figure 1 of Chapter 5 and Figure 
8 of this section) and are especially difficult to 
observe. 

Theoretical and experimental studies on the rate 
of rise of bubbles in still water are summarized in 
Figure 8. The rate of rise of the bubbles which are 
most effective in scattering is seen to be about 1 yd/ 
minute. These results for still water do not apply 
directly to wakes or turbulent water. The long-lived 
bubbles observed in the USNRSL pool did not show 
any marked tendency to rise, but were carried in 
irregular paths by the motion of the water. This is 
analogous to the effect of air currents in keeping 
dust from settling. It is reasonable to suppose that 
the moderate turbulence in an old wake will have 
this same effect and prevent the disappearance of 
the bubbles. 


6.2.2 Propeller Cavitation as a 
Source of Bubbles 

The second objection is based on the fact that 
echoes are obtained from the wakes of submerged 
submarines and the idea that most of the bubbles 
in a wake come from the breaking bow wave. The 
aerial photographs strongly suggest that this idea is 
not correct, since most of the foam appears to come 
directly from the screws. This is borne out by the 
observation that the wake laid by a vessel under 
sail is less acoustically active than the wake of the 
same vessel under power. 

Hence it is probable that most of the bubbles are 
caused by cavitation at the propellers. Photographs 
of this phenomenon are shown in Figures 9 and 10. 
The bubbles are seen to be formed far from the air- 
water interface and are not sucked under from the 
atmosphere. The mechanism of cavitation is appar- 
ently very similar to that of boiling. Because of the 
motion of the screws, the hydrostatic pressure is 
reduced; the boiling point of water is lowered by 
this reduced pressure, so that it is below the 
actual temperature of the water, and boiling oc- 
curs. For example, pure water will boil at 60°F if 
the pressure is reduced much below one-sixtieth of 
an atmosphere. 


THEORY OF THE ACOUSTIC PROPERTIES OF WAKES 


121 



Figure 9. Cavitating propeller. The water in the jet 
is moving away from the observer. The back of each 
blade is half covered with cavitation bubbles and a cavi- 
tation void which extends for some distance behind the 
blade, whereas the face of each blade is clean. (Photo- 
graph by David Taylor Model Basin.) 



Figure 10. Tip vortices emanating from a propeller. 
The combination of the rotation of the propeller and 
the flow of the water in the jet from left to right gives 
a spiral pattern to the vortices. (Photograph by David 
Taylor Model Basin.) 


However, sea water is not pure. In the present 
connection, dissolved air is the most important im- 
purity. This is present in such quantities that sea 
water will boil at 60°F whenever the pressure is re- 
duced much below one atmosphere. The bubbles 
produced by this boiling are filled principally with 
air, rather than water vapor. Once formed, these 
bubbles are apparently quite stable, i.e., the rate at 
which the air is redissolved is very slow. 

Laboratory experiments 1 show that the diameter 
of the bubble decreases at a constant rate at any 
given depth. Figure 11 shows that at a depth of 50 m 
the diameter of a bubble decreases 1 mm every 10 
minutes. Thus, a bubble initially 1 mm in diameter 
would require 9 minutes to reach a diameter of 0.1 
mm and a further 1 minute to reach a very small 
diameter or disappear. 

It appears likely that, even in the wakes of surface 
vessels, much of the foam is the result of cavitation, 
and that only a part of it is caused by air dragged 
under from the atmosphere. In the wakes of sub- 
merged submarines, the only sources of air other 
than cavitation might conceivably be a leaky high- 
pressure air line. 



Figure 11. Rate at which the size of bubbles varies at 
various depths. The curve shows the time required for 
the diameter of a bubble to decrease 1 mm. 


6.2.3 Dependence of Cavitation on 
Depth and Speed 

It is found that cavitation depends critically on 
propeller rpm. A given propeller at a given depth 
of submergence will produce no bubbles unless its 
speed exceeds a certain critical value. Let No rpm 
be this critical value; when the speed exceeds No, 



122 


WAKES 


the number of bubbles formed increases very rapidly, 
but not according to any known law. 

The critical speed itself, however, depends in a 
simple manner on h, the depth of the propeller be- 
neath the sea surface. This dependence is given by 

K 

— = constant. (1) 

h 

Thus, if a given propeller begins to cavitate at 50 rpm 
when at a depth of 15 ft, it will begin to cavitate at 
100 rpm when at a depth of 60 ft, and not until 
200 rpm when at a depth of 240 ft. 

The constant in equation (1) depends on the 
design of the propeller, and on any accidental changes 
in its shape that may occur in service. A scratch or 
nick caused by some accident will usually reduce 
the value of the critical speed very appreciably. One 
remarkable property of cavitation is that the bubbles 
themselves scratch and scar the metal surface on 
which they are formed. 2 


DEPTH, FT 


-I 

u 

> 

UJ 

_l 






o- 60 KC 

• 50 KC 

^ 40 KC 

A* 30 KC 

c 

0 

5 

O < 

1 





•— 

/ 

/ 

i • 
i 

I 


' \° 




i • 

*/ 

✓ 

. 

W 

0 • 



• t> t> 

/ 

(4 

w, t 


* 

► \ 

\ 

. X 

\ 



* 

\ A 

'■J 

, 

\ 

\ 



A 

j 

\ 

, \ , 

■ \ 

\ 

V 

k \ 

\ 






> \ 

\ 



Figure 12. Dependence of level of scattered sound on 
depth. The sound was scattered from the wake of a 
10-in. propeller run at 1,600 rpm. The direct signal 
was constant for each frequency. 


This theory of the connection between cavitation 
and the acoustic properties of wakes has certain 
consequences that can be qualitatively checked. 
Thus the wake of a submerged submarine should 


return echoes, but they should be considerably 
weaker than when the ship is moving on the surface. 
They should also become progressively weaker as 
the depth of submergence increases. Finally, they 
should increase rapidly with propeller speed. All 
these conclusions are in general agreement with 
experience. 

Experiments designed to test the theory were 
performed by Woods Hole Oceanographic Institu- 
tion. A small propeller (10 to 20 in. in diam) was 
operated when suspended from a wharf at various 
depths up to 60 ft. The possibility of atmospheric 
air being entrained in its wake was thus definitely 
excluded. No echoes were obtained when the pro- 
peller speed was below the critical speed for cavita- 
tion; echoes were obtained at higher speeds. The 
wake was also observed to attenuate sound passing 
through it. Figure 12 summarizes the measured scat- 
tering of sound by the 10-in. propeller, as a function 
of depth and frequency. 

The propellers are probably not the only source 
of cavitation bubbles. Since the ship as a whole is 
moving through the water, cavitation can occur at 
other places. In general, the smaller the object, the 
lower is the critical speed at which cavitation occurs. 
Thus small fittings or hand rails on the deck of a 
submarine may become sour ces of cavitation bubbles 
when submerged. This effect is probably the explana- 
tion of the blackening in the upper part of Figure 6. 
Such “conning tower wakes” probably contribute 
only slightly to the reflection of sound from the 
submarine, although the only experimental evidence 
on this point is that of Figure 6. 


6.2.4 The Propagation of Sound in 
Water Containing Bubbles 

The theoretical discussion of the acoustic prop- 
erties of water containing air bubbles is complicated, 
and the studies are not complete. 3 In order to present 
the general ideas of the theory without confusion, 
it is convenient to introduce certain terms for the 
description of water containing bubbles. 

In foamy water , the average distance between 
neighboring bubbles is less than the average diameter 
of the bubbles. In the extreme case, the walls separat- 
ing the bubbles may be very thin, as in the case of 
soap suds. The acoustic theory of foamy water has 
not been studied at all, but this is no serious lack, 
since wakes probably contain foamy water only at 


THEORY OF THE ACOUSTIC PROPERTIES OF WAKES 


123 


the air-water surface, where the bubbles tend to 
accumulate. 

In bubbly water } the average distance between 
neighboring bubbles is considerably greater than the 
average diameter of the bubbles, but much less than 
the wavelength of the sound involved. For practical 
purposes, the water may be considered to be bubbly 
if it contains less than one part per 1,000 (by volume) 
of air, and foamy if it contains much more than this. 
The bubbles are dispersed if the average distance 
between neighbors is greater both than one wave- 
length of the sound and than the average diameter. 
Thus a portion of a wake may be dispersed for super- 
sonic frequencies and bubbly for sonic frequencies. 

It would be very useful to have information con- 
cerning the foamy, bubbly, and dispersed regions of 
typical wakes. Unfortunately, there is relatively little 
information of this sort other than that which can 
be obtained from the inspection of aerial photographs 
or deduced indirectly from acoustic measurements. 
It is probable that the wake reaches the dispersed 
state some 5 to 10 ship-lengths astern of the screws, 
and is foamy only in the immediate neighborhood 
of the screws, or of the air-water surface. 

625 Scattering and Absorption of 
Sound in Wakes 

The theory of dispersed wakes is very similar to 
the theory of reverberation, with the exception that 
somewhat greater attention must be given to detail. 

Consider a single bubble of diameter d , in a region 
where the flow of acoustic energy is F w/yd 2 . This 
bubble will remove power from the beam at the rate 

P = Fcq watts removed, (2) 

where a 0 will be called the total effective cross section 
of the bubble. Of this power, a fraction a will be 
reradiated as sound, so that 

a P = Fv.(jq = Fa watts scattered. (3) 

The quantity a = ocao will be called the scattering cross 
section of the bubble. It is the quantity which was 
discussed in Section 5.4 and may be very much greater 
than 7r d 2 (see Figure 1 of Chapter 5) . The remainder 
of the power will be converted into heat, i.e., ab- 
sorbed by the air of the bubble and, to a lesser 
extent, by the water surrounding it ; thus 

(1 — a) P = F (1 — a) a 0 = Fa a watts absorbed. (4) 


The quantity a a is called the absorption cross section 
of the bubble. Note that 

<tq = a-\- a a . (5) 

There are theoretical reasons for believing that a 0 /a 
is about 10. 

Figure 13 shows the variation of the scattering 
and absorption cross sections with the diameter of 
the bubble, the sound frequency being 24 kc. The 
abscissa shows the ratio of the actual diameter of 


d/d 0 



Figure 13. Variation of scattering cross section and 
absorption cross section of a bubble with its diameter 
for 24-kc sound. The abscissa is the ratio of the actual 
diameter of the bubble to the resonance diameter cal- 
culated from equation (11) of Chapter 5. The ordinate 
is the ratio of the scattering cross section or absorption 
cross section, respectively, to the geometric cross sec- 
tion of the bubble. 

the bubble to the resonance diameter calculated 
from equation (11) of Chapter 5. Note that the 
absorption of sound by the bubble causes a slight 
shift of the resonance peak to smaller diameters than 
given by that equation. The ordinate is the ratio 
of the scattering or absorption cross section to the 
geometric cross section of the bubble. 

In the theory about to be developed, it will be 
shown that it is the total effective cross section ao, 
which determines the screening caused by a wake, 
while the strength of the wake echo is determined 
by the scattering cross section a. 

Even though the wake is dispersed, so that the 
distance between neighboring bubbles is large, the 
whole wake will still contain many bubbles. Some 
of these will not be in the sound beam, and thus can 
be neglected. This is indicated diagrammatically in 
Figure 14. In plan, the wake is shown as a parallel 
strip, the sound beam as a divergent one. In section, 


124 


WAKES 



SEA 



SECTION A-A 

Figure 14. Diagram showing intersection of sound 
beam and wake in plan (upper figure) ; the lower figure 
shows section A-A. F=energy flow in incident beam; 
F t = energy flow after traversing the wake; 9 = angle 
between axis of sound beam and axis of wake; <t> = 
angular half width of sound beam; r = distance from 
sonar to wake; h = vertical dimension of wake; w = width 
of wake. 

the sound beam is shown as a sharply bounded circle, 
and the wake as a sharply bounded layer. These 
sharp boundaries are probably not realized in prac- 
tice, but are convenient idealizations. Only those 
bubbles in the intersection of the two, i.e., in the 
region marked “active volume,” contribute to the 
acoustic effects. The total number of bubbles that 
are effective thus depends on w, the width of the 
wake; on 0, the angle between the wake and the 
axis of the sound beam; and on A, the area of the 
sound beam that is intercepted by the wake. 

The theory of wide wakes is rather different from 
the theory of narrow wakes, so that the distinction 
between the two kinds will be considered in some 
detail. Figure 15 is an enlarged schematic of the 
Section AA of Figure 14. The position of each bubble 


is indicated by a dot; the circles surrounding the 
dots are supposed to have the area o- 0 appropriate 
to each bubble. (Scale relations are obviously ex- 
aggerated.) The total number of bubbles in the active 
volume is small in the case illustrated, so small that 
their projected areas overlap in only a very few 
cases. When this condition is fulfilled, the wake will 
be called narrow. When, on the other hand, there 



Figure 15. Enlarged schematic of section A-A of Fig- 
ure 14. The dots represent bubbles; the circles sur- 
rounding the dots are supposed to have the area <r 0 
appropriate to each bubble. (Scale relations are 
obviously exaggerated.) 

are so many bubbles that their projected areas usu- 
ally overlap, the wake will be called wide. It should 
be noted that this definition depends on the total 
number of bubbles in the active volume, not merely 
on the number of bubbles in unit volume. 


6 2 6 Theory of Narrow Wakes 


The Screening Action of Wakes 


The approximate calculation of the screening 
effect and target strength of a narrow wake can be 
made as follows. 

Let N = average number of bubbles in unit vol- 
ume of the wake (1/yd 3 ), 
o-o,o- = average total and scattering cross section 
of one bubble (yd 2 ), 
w = geometric width of wake (yd) (see 
Figure 13), 

0 = angle between axis of sound beam and 
axis of wake, 

A = area of sound beam intercepted by the 
wake (yd 2 ) (see Figure 12). 


Then the active volume will be approximately given 
by 


Aw 
cos 0 


(yd 3 )- 


( 6 ) 


THEORY OF THE ACOUSTIC PROPERTIES OF WAKES 


125 


The total number of active scatterers will be N times 
this volume, and their effective area will be 


N ao Aw 
cos 0 


(yd 2 ). 


(7) 


In this calculation, all effects caused by the over- 
lapping of the projected areas in Figure 15 have 
been neglected, since the wake is narrow. The total 
power removed from the sound beam will be 
FNaoAw 

(watts removed). (8) 

cos 0 


The power in the incident beam is FA, and after it 
has traversed the wake, the power in the beam is 
F t A; consequently, 


F t A = FA 


1 — Na 0 w 
cos 0 


(9) 


The ratio of the transmitted energy flow to the 
energy flow incident on the wake measures the trans- 
mission loss in traversing the wake. It obviously 
applies only to that part of the sound beam that has 
passed through the wake, and not to the part that 
has passed under it. 

The transmission loss H in decibels is given by 


F t 1 — Naow 

H = 10 log — = 10 log . (10) 

F cos 0 


The Scattering Action of Wakes 


The total power removed from the beam by scat- 
tering will be obtained from equation (8) on replacing 
the total cross section ao by the scattering cross 
section a, 

FNaAw 

(watts scattered). (11) 

cos 0 

At a great distance r from the active volume of the 
wake, this scattered power will be spread over a 
sphere of area 47rr 2 . Hence, the average energy flow 
at this distance will be 


FNaAw 

— (w/yd 2 ). 

47rr 2 cos 0 


( 12 ) 


Comparing this with equations (6) and (9c) of Chap- 
ter 5, which are 


F s = 


Fa 

i^ 2 ’ 


T = 10 log 



it is seen that the target strength of the wake is 

/ NaAw\ 

T= 10 log . (13) 

\ 471-cos 0/ 

This expression is noteworthy in that it contains 
A, the cross section of that part of the sound beam 
intercepted by the wake. This was not true in the 
case of the screening ratio F t /F. Since the sound 
beam diverges, A will increase with the range of the 
wake from the sonar projector, so that the target 
strength of a distant wake will be greater than that 
of a nearer one, all other things being equal. 


The Strength of the Wake 


The accurate calculation of A is complicated, and 
the values of many of the quantities entering it are 
uncertain. Consequently, a very rough calculation 
will suffice for the present. Let the angular half- 
width of the sound beam be <t> radians. Then the 
diameter of the beam at a range of r yd from the 
sonar will be 2 r<f> yd. If the wake has a vertical 
dimension of h yd (see Figure 14), an approximate 
expression of A is 


A = 2 r<f>h. 


Substituting this in equation (13), one obtains 


/ Nawh \ 

T = 10 log ( — — j + 10 log 



(14) 

(15) 


This expression has been separated into two terms, 
the first of which contains only quantities character- 
istic of the wake, the second only quantities describ- 
ing the position of the sonar, and the bearing and 
width of the sonar beam. The first term of equation 
(15), 

/ Nawh\ 

W =10 log [—£—) db, ( 16 ) 


is called the strength of the wake. Since 2 r<j> is essen- 
tially the length of the wake that lies in the sound 
beam, W may be interpreted as the target strength 
of 1 yd of the wake. 

One objective of the research on wakes has been 
to determine IF for the wakes laid by various types 
of vessels under various conditions. 


6 . 2.7 Theory of Wide Wakes 

In the case of wide wakes, the total number of 
bubbles in the active volume is so great that there 
is much overlapping of the projected areas in Figure 


and 


126 


WAKES 


15. If equation (8) were used to calculate the power 
removed from the sound beam, this quantity would 
be greater than FA ; the wake would, according to 
this formula, remove more power than was incident 
on it. This is obviously absurd, and results from 
the neglect of the overlapping projected areas. 

One might be tempted to allow for the overlapping 
by assuming that the bubbles nearest the source of 
sound cast shadows on those farther away, thus 
rendering them ineffective in removing power from 
the beam, or in returning echoes. Without going 
into the details of the calculation, this would replace 
equation (10) by the equation 


Ft 


exp 



and replace equation (13) by 


T = 



(17) 


(18) 


These equations are free from the obvious absurd- 
ity of equations (10) and (13) when applied to wide 
wakes and are probably reasonably accurate. Several 
theoretical objections to them will be discussed, since 
the discussion brings out important characteristics of 
wakes. In the first place, obstacles smaller than one 
wavelength in diameter do not cast sharp shadows, 
even though a cloud of them does weaken the train 
of waves passing through it. In the second place, 
sound scattered by one bubble may reach a second 
bubble and be scattered a second time. Neither of 
these facts are considered in the derivation of 
equations (17) and (18). 

Theoretically, the possibility of multiple scattering 
is the more important reason for doubting the 
validity of these equations. They are based on the 
assumption that most of the sound energy is travel- 
ing in the direction of the incident wave, and that 
sound traveling in other directions has been scattered 
only once. If the scattering cross section <j were 
much greater than the absorption cross section a a 
(or, in other words, if a 0 were about equal to a), this 
would not be true. In the interior of a wide wake, 
most of the sound would have been scattered many 
times; and waves traveling in all directions would 
be present. The most common example of this phe- 
nomenon is presented by the sun’s light on a foggy 
day: from the interior of the fog, it is impossible to 
determine the direction of the sun. A further con- 
sequence of the diffuse illumination is that even 
large objects cast no shadows. To pursue the analogy, 


the interior of a narrow wake would be similar to a 
hazy day, in which the sun can be seen distinctly 
but is dimmed by the haze. 

It is probable that this condition is not present 
in wakes. As has been remarked, the ratio of a to <r 0 
is of the order of magnitude 0.1. Consequently most 
of the energy intercepted by a bubble will be ab- 
sorbed and only a small part will be scattered. By 
the time this process has been repeated, the multiply- 
scattered radiation will be so weak as to be negligible. 
The analogy to daylight in a fog breaks down under 
these conditions, and the situation is rather more 
like looking at the sun through a dark glass. The 
direct, unscattered radiation is weak, but the scat- 
tered radiation is even weaker. 


6 2 8 Theory of Bubbly Wakes 

Change in Velocity of Sound Due to Bubbles 

The mathematical theory of bubbly water is 
similar to the theory of the index of refraction of 
light in a gas composed of separated molecules. In 
both cases, the velocity of the waves is determined 
by the number and nature of the particles in their 
path. 

Small amounts of air bubbles can produce very 
appreciable changes in the velocity of sound. There 
is little experimental evidence on this point, and the 

TT d/x 



of ratio of circumference of bubble to wavelength of 
sound. A C = change in velocity of sound. P = parts per 
million of air bubbles, by volume. d = diameter of 
bubble. X = wavelength of sound. 

theory is complicated by the fact that the bubbles 
are not all the same diameter. Figure 16 shows the 
theoretical change in the velocity of sound caused 


THEORY OF THE ACOUSTIC PROPERTIES OF WAKES 


127 


by 1 part /million (by volume) of air bubbles, as a 
function of (ir d/\), where d is the diameter of the 
bubbles and X the wavelength of the sound. The 
wavelength is to be" measured in bubble-free water, 
and it is assumed that the air in the bubbles is at 
a pressure of one atmosphere. 

For other concentrations, the change in the vel- 
ocity of sound is proportional to that shown in the 
figure, provided that the change is not more than a 
few hundred yards per second. Concentrations pro- 
ducing larger changes than this require special com- 
putations that have not yet been carried out. 

The significance of this changed velocity of sound 
for the theory of wakes is not clear. If the wake had 
very sharp boundaries, the abrupt change in velocity 
would result in reflection of the sound. However, 
the boundary of an actual wake is probably never 
sharp, and hence this reflection will not occur. How- 
ever, sound rays passing through the wake will be 
refracted. The angular deflection of the rays is 
difficult to determine, either experimentally or the- 
oretically. 

Scattering and Absorption 

Apart from this change in the velocity of sound, 
scattering and absorption also occur. Qualitatively, 
these effects are entirely similar to those in dispersed 
wakes. The quantitative differences have not been 
studied theoretically, but some guesses concerning 
the results of such a study can be made. The in- 
dividual bubbles in a dispersed wake have been 
assumed to act, each as though the others were not 
present. In bubbly water, this will no longer be the 
case. One effect of this “cooperation” among the 
bubbles is the change in the velocity of sound. 

Other Cooperative Effects 

It is possible that other cooperative effects become 
important in bubbly water. For example, consider 
two bubbles, widely separated, having scattering 
cross sections a' and a". If these same bubbles are 
brought close together, so that the distance between 
their centers is not more than 2 or 3 diameters, the 
numbers </ and a" will cease to have any signif- 
icance. It will not be possible to distinguish between 
the energy scattered by one and that scattered by 
the other. Moreover, the total amount of energy 
scattered will not be determined by the sum a' -f- cr", 
but will depend also on the distance between their 


centers. Thus, it is certain that the theory of foamy 
water will be primarily concerned with cooperative 
effects. Bubbly water is a transition stage; it may 
be that cooperation in scattering begins when the 
average distance between bubbles becomes compar- 
able to one wavelength, for it is certain that coopera- 
tion is well developed when the distance becomes 
comparable to one diameter. 

4 

6.2.9 The Importance and Interpretation 
of Scattering Experiments 

Historically, the study of scattering and absorp- 
tion has played an important part in the development 
of various branches of physics. This is especially 
true of those branches dealing with radiations that 
are not perceptible by the unaided human senses, 
such as X rays, a rays, /3 rays, y rays, cosmic rays, 
and more recently, neutron rays. The scattering of 
visible light explains the color of the clear sky and 
other meteorological phenomena. The scattering of 
sound waves had not been studied in any systematic 
manner prior to World War II. During the war, such 
studies were begun but are still far from complete. 

Modern knowledge of the structure of matter, 
atoms, and nuclei is largely based on scattering ex- 
periments. It is unlikely that experiments on the 
scattering of sound and radio waves will contribute 
much to this fundamental body of knowledge con- 
cerning the imperceptible structure of matter. It is 
almost certain, however, that they will contribute 
much to the knowledge of the inaccessible parts of 
the ocean and the atmosphere. It is for this reason 
that studies of reverberation and of the scattering 
of sound by wakes are considered to be very import- 
ant, even apart from immediate practical objectives. 

The literature on the scattering of other forms of 
radiation is voluminous, and there is no one source 
book. The interpretation of the experiments has been 
the subject of much careful thought, and has resulted 
in many major advances in knowledge. However, 
examples of misinterpretations on the part of con- 
scientious and able experimenters are also numerous. 
For this reason, some words of caution are appro- 
priate at this point. 

The most common error is the measurement of 
extraneous radiation along with that which it was 
intended to measure. Thus, in measuring the inten- 
sity of sound transmitted through a wake, it is most 
important to shield the hydrophone from all sound 


128 


WAKES 


that passes beneath the wake (see Figure 14). This 
may be a difficult thing to accomplish. 

The interpretation of many laboratory experiments 
has been simplified by the use of opaque screens to 
shield the detector from extraneous radiation. Some- 
times these screens have not been completely opaque, 
and often their edges have been the source of scat- 
tered radiation. In performing scattering experiments 
at sea, it is not possible to use such screens, so that 
the possibility of extraneous sound is particularly 
great. 

Another error is the application of theoretical 
equations to circumstances that do not conform to 
the assumptions made in deriving them. Thus, equa- 
tions (17) and (18) are derived on the assumption 
that the source and receiver of sound are both well 
outside the wake and are highly directional. If one 
or both are in the wake, or even if the receiver is 
near the wake, these equations may be considerably 
in error. If the receiver is nondirectional and is in or 
near the wake, it must not be assumed that all of 
the sound measured comes from the direction of the 
source. The scattered sound may obviously come 
from any direction. Moreover, when a transducer is 
in a wake, its diaphragm may be covered with adher- 
ing bubbles, and these will have a marked influence 
on its sensitivity or power output. 

6.3 EXPERIMENTAL RESULTS 

6 . 3.1 Transmission of Sound through 
Wakes of Surface Vessels 

A series of experiments on the wakes of destroyers 
and destroyer escorts was performed by the Uni- 
versity of California Division of War Research 
[UCDWR]. 4 The procedure was as follows. One ves- 
sel carried a hydrophone and was dead in the water, 
while the destroyer ran past it on a straight course 
at a fixed speed. As soon as the destroyer had passed, 
a small launch got underway and carried the sound 
source from one side of the wake to the other. In 
this way it was possible to measure the intensity of 
the sound both when the wake intervened between 
source and receiver, and when the source was on the 
same side of the wake as the receiver. After making 
allowance for the difference in range when the source 
was on one side or the other of the wake, the apparent 
transmission loss caused by the wake was calculated. 


However, it is not certain that the result is free 
from error. In the first place, when the sound source 
is on the far side of the wake, it is possible that some 
sound may pass under the wake and reach the hy- 
drophone. This error was minimized by suspending 
both source and hydrophone at about one half the 
depth of the wake. In spite of this precaution, it 
must be emphasized that the values of transmission 
loss so obtained are possibly too low. 

This source of error can be eliminated by making 
the measurement while the source is in the wake, 
but then the measurement may be too large because 
of the effect of bubbles in reducing the output of 
the source. To some extent, this will be balanced 
out because only part of the wake will be between 
source and receiver. The true value will probably 
lie between the two measured values. 

The results of an extensive program have been 
summarized by the following equations : 

H = 1.5(7/)* -3.07 7 (19) 

when the source is on the far side of the wake, and 
H = 2.4(7/)* -4.8T (20) 

when the source is in the wake. The symbols have 
the following meanings: 

H = transmission loss (db), 

V = speed of destroyer (knots), 

/ = frequency of sound (kc), 

T = age of wake (minutes). 

These equations have no theoretical foundation, 
and the experimental data which they summarize 
are rather scattered. The results of a typical experi- 
ment are compared with equation (19) in Figure 17. 
Eight experiments of this kind were performed at 
speeds of 10, 15, 20, and 25 knots. Three frequencies 
(3, 8, 20 kc) were used in all, and a fourth (40 kc) in 
a few of the runs. Equations (19) and (20) agree 
with the results of all these experiments in much 
the same manner as with the one shown in detail 
on Figure 17. 

6.3.2 Wake Strengths — Surface Vessels 

Dependence on Age of Wake 

Early experiments were performed with a single 
vessel (the USS Jasper ) which ran on a straight 
course, then circled and echo ranged on its own 
wake. 5 These experiments showed that the level of 
the echo decreased fairly rapidly with the age of 


EXPERIMENTAL RESULTS 


129 


ACE OF WAKE, MINUTES 



Figure 17. Comparison of observed values of trans- 
mission loss in wakes with values calculated from 
= 1.5 (F/)*-3.0 T. 


the wake; the results of various experiments ranged 
from 1.5 db/min to 8 db/min, with an average of 
about 4 db/min. The levels of the echoes were com- 
pared with those of reverberation on the same day 
at the same range from the sonar. On one day, this 
range was about 235 ft and the echoes were about 
40 db higher than either volume or surface reverbera- 
tion. These two kinds of reverberation were about 
equal at this range. On another occasion, the range 
was 140 ft and the echo was 17 db higher than 
surface reverberation. A sea state 2 and wind force 
3 prevailed on this occasion. In view of the variability 
of reverberation from day to day, these observations 
have little absolute significance, but serve to give 
some idea of the strength of echoes from the wake 
of a small slow-speed vessel. The values obtained for 
the rate of decrease of the wake echo have greater 
claim to validity, and are in good agreement with 
all other observations. 


The difficulties inherent in performing experiments 
on wakes at sea led to an extended series of experi- 
ments in San Diego Harbor, a 40-ft motor launch 
being used to lay the wakes which extended from 
the surface to a depth of about 5 yd. 6 There was 
some evidence that sound reflected from the bottom 
increased the strength of the echo; in order to mini- 
mize this effect, only echoes obtained at ranges less 
than 100 yd are included in the following averages. 

Echoes were obtained using 15-, 24-, and 30-kc 
sound. It was found that these did not reach their 
maximum value until some time after the passage 
of the launch through the sound beam. Average 
values of the time of the maximum echo are shown 
in the second column of Table 1. Thereafter, the 
echo intensity diminished at an average rate of about 
7 db/min for all three frequencies. The wake strength 
(see Section 6.2) at the time of the maximum echo 
level was computed for each experiment, and aver- 
age values are shown in the third column of Table 1. 


Table 1. Dependence of wake strength on age of wake. 



Time of 

Wake strength at 

Frequency 

max. echo 

time of max. echo 

(kc) 

(sec) 

(db) 

15 

30 

-2.9 

24 

50 

+ 3.1 

30 

70 

+ 8.4 


Figure 18 serves to give further information con- 
cerning the behavior of wake echoes. The early 
period, during which the echo from the wake increases 
in level, is clearly evident, as is the later period 


AGE OF WAKE, MINUTES 



Figure 18. Variation of the wake echo level with age 
of the wake, for various ping lengths at 24 kc. 


130 


WAKES 


during which the echo level decreases at a rate of 
about 1.8 db/minute. 

During the work in San Diego Harbor, echoes 
were obtained from the wakes of passing vessels. 
Values of the wake strengths of these are shown in 
Table 2. While there are marked differences from 
vessel to vessel, there appears to be a tendency for 
the wake strength to increase with frequency. 


Table 2. Wake strengths of various types of vessels. 


Vessel 

15 kc 

Wake strength 
24 kc 

30 kc 

Tanker 

8.1 

7.7 

9.0 

Fishing boat 

0.7 

10.7 

9.0 

Fishing boat 

0.0 

-0.6 


Fishing boat 


-0.4 


Kelp barge 

7.3 

5.5 

12.2 

Kelp barge 

4.5 

9.1 

14.3 

Launch (50-ft) 

2.7 

7.9 

12.9 

Transport 

18.9 

17.5 

22.9 

Tank boat 

10.9 

10.3 

14.7 


All later work was conducted at sea, in order to 
avoid the disturbing effect of bottom reflections. 
Figure 19 shows echoes from the wake of a destroyer 
(DD, 5th Group, 1917) traveling at 15 knots. The 
sound frequency was 24 kc,« and the three oscillo- 
grams marked 41, 42, 43 were obtained with an 80- 
yd ping length, about 20 sec after the destroyer’s 
screws had passed through the sound beam. Oscillo- 
grams 51, 52, 53 were obtained with a 9-yd ping 
length, about 15 sec later. The duration of the echo 
from the long ping is almost entirely determined by 
the ping length; that of the echo from the short ping 
shows definite elongation caused by the extent of 
the wake. Oscillograms 173, 174, 175, obtained with 
the short ping 870 sec after passage of the destroyer, 
show the increased echo elongation and the decreased 
amplitude of the echo caused by this spreading and 
dispersion. 


Table 3 summarizes measurements of similar oscil- 
lograms obtained from the wakes of a number of 
vessels, using ping lengths of 8 to 24 yd. The speeds 
of the vessels were all within the normal range of 
operation. 

Dependence on Ping Length 

Figure 18 also brings out a dependence of echo 
level on ping length. The theoretical discussion has 
emphasized the analogy between wake echoes and 
reverberation. Essentially, the wake is a part of the 
ocean from which the reverberation is especially 
high. If the ping length is shorter than the width of 
the wake, the distinction between reverberation and 
wake echoes disappears. The number of scatterers 
returning echoes at any moment is determined, not 
by the extent of the wake, but by the ping length. 
Under these conditions, illustrated by oscillograms 
173, 174, 175 of Figure 19, the echo level should be 
proportional to ping length. If, on the other hand, 
the ping length is long compared to the width of the 
wake (see 41, 42, 43 of Figure 19), the echo level 
should be independent of ping length. These effects 
are also evident on Figure 18. 

6.3.3 Wake Strengths — Submarines 

Experiments on the wakes of submerged sub- 
marines encounter many difficulties. The problems 
of navigation and seamanship involved in the man- 
euvers are not always solved successfully, even by 
the ablest submariners. The low levels of the wake 
echoes, together with these practical difficulties, ac- 
count for the conflicting reports that have been made 
on the subject. 

On one occasion, echoes from the wake of an S-type 
submarine were recorded with standard echo-ranging 


Table 3. Dependence of wake strength on wake-laying vessel. 


Type of 
wake vessel 


24 kc 



60 kc 


Average W 
(db) 

Standard deviation 
of W (db) 

Number of 
wakes 

Average W 
(db) 

Standard deviation 
of W (db) 

Number of 
wakes 

CVE’s and AP’s 

- 7.7 

4.1 

5 




DD’s and DE’s 

- 9.6 

6.3 

5 

+ 7.9 

1.1 

2 

Laboratory yachts 
(Scripps & Jasper) 

-13.6 

2.6 

5 

+ 1.6 

3.0 

8 

Small boats 

-18.2 

2.0 

2 

-3.7 

2.1 

2 


EXPERIMENTAL RESULTS 


131 



Figure 19. Echoes from the wake of a destroyer (DD, 5th group, 1917) traveling at 15 knots. Frequency = 24-kc. 
Oscillograms marked 41, 42, 43 were obtained with an 80-yd ping length, about 20 sec after the destroyer’s screws 
had passed through the sound beam. Those marked 51, 52, 53 were obtained with a 9-yd ping length, about 15 sec 
later. Oscillograms 173, 174, 175 were obtained with the short ping 870 sec after the passage of the destroyer. They 
show the increased echo elongation and the decreased amplitude of the echo caused by this spreading and dispersion. 


gear operated at 24 kc. When running at a depth of 
45 ft, contact was maintained with the wake at a 
distance of 3,000 ft astern of the screws. At depths of 
90 and 125 ft, the lengths of the contacts were 700 
and 300 ft, respectively. 

On a second occasion, it was attempted to use a 
recording echo sounder for the study. As noted above 
(Figures 6 and 7), this instrument had been success- 
fully used in the study of the wakes of surface vessels. 
Consequently, it was mounted on a launch, and the 
submarine (fleet-type) ran on a straight course de- 
signed to carry it directly under the launch. This 
maneuver proved difficult to execute, but echoes 
from the hull of the submarine were obtained on 
several occasions. The depth of the submarine varied 
from 65 to 200 ft. On no occasion were echoes from 
the wake obtained at distances more than 50 to 100 
ft astern of the screws. 

It had been hoped that this experiment would 
show whether the wake had a tendency to rise to 
the surface, as might be expected if bubbles are the 
primary cause of its acoustic activity. The results 
were inconclusive. It has been reported that, on 
several occasions, the wake of a submarine running 
at a depth of 45 to 60 ft could be seen from the deck 
of a nearby surface vessel. This visibility was ap- 
parently due more to turbulence, which disturbed 
the surface, than to bubbles. 

On a third occasion, some fifteen experiments were 
performed to measure the wake strength of a fleet- 


type submarine running at various depths from 45 
to 400 ft. None of these yielded echoes that were 
positively identified as caused by the wake, although 
echoes from the hull of the vessel were obtained. 
Some few echoes may have come from a short dis- 
tance astern of the screws. Frequencies of 20 kc and 
45 kc were used; 45-kc echoes from the wake would 
have been recorded unless they were more than 14 
db below those from the submarine itself. At 20 kc, 
the difference must have been more than 28 db. 

The operational problems were reduced to man- 
ageable proportions by the following procedure. The 
submarine started on the surface, running a course 
parallel to that of the echo-ranging vessel. The latter 
ran at a slow speed, so that the submarine overtook 
it and passed through the sound beam while still on 
the surface and at a range of 100 to 300 yd. About 
90 sec after passage, the submarine dived rapidly to 
90 ft and slowed down. Simultaneously the surface 
vessel increased speed, so as to overtake the sub- 
merged submarine about 10 minutes later. It was 
found that these operations could be carried out 
satisfactorily except that it was difficult to adhere 
to the prearranged time schedule, and that the sub- 
marine’s submerged course often diverged apprecia- 
bly from that of the surface vessel. The timing of 
events was critical because of the limited supply of 
film in the magazine of the recording oscillograph. 

Data recorded during such an experiment are 
summarized in Figure 20. It is seen that the wake 


132 


WAKES 


TIME, MINUTES 



Figure 20. Wake strength of submarine. The lower half of the figure shows the distance astern in feet. 


strength while running on the surface was — 10 to 
— 15 db. This was momentarily increased as the 
echo-ranging vessel passed the site of the dive, where 
the venting of air from the ballast tanks presumably 
increased the bubble content of the wake. After the 
submarine reached the depth of 90 ft, the wake 
strength varied between — 20 and — 30, even while 
the distance astern remained practically constant at 
about 900 ft. As the echo-ranging vessel overtook 
the submarine, the wake strength again increased 
to — 20 db. 

The results of other experiments with submarines 
are listed in Table 4. Ping lengths of 8 to 24 yd were 
used in all of the work summarized. It is seen that 


Table 4. Wake strengths of submarines 


Submarine 

type 

Freq. 

(kc) 

Wake strength 
surfaced 

9 knots 
(db) 

Wake strength 
submerged 

6 knots 
(db) 

Depth 

(ft) 

S 

60 

-18 

-26 

90 

S 

45 

-13 

-24 

90 

Fleet 

45 

-13 

-20 

90 

s 

45 


-33 

45 

s 

20 


-20 

45 


the strengths of submarine wakes are very small, 
even when the vessel is running on the surface. This 
is probably to be explained by the low speeds at 
which the vessel moves. 


PART II 


ECHO RANGING 


I N echo ranging, a sound signal is projected into 
the water, in the expectation that it will strike 
a target and be reflected back to the transmitter. 
The time interval between the emission of the signal 
and the detection of the echo gives the range of the 
target; if c is the velocit 3 r of sound in the sea and t 
the elapsed time between signal and echo, the range 
r is given by 


ct 



Provided the emitted sound energy is concentrated 
in a narrow beam, the bearing of the target can be 
determined from the orientation of the transmitter. 
If the transmitter can be rotated about a horizontal 
axis, the depth of the target can also be determined. 
Various characteristics of the echo can provide in- 
formation concerning the size, speed, and aspect of 
the target. 

Discussion of the manifold problems of echo rang- 
ing centers around the four basic ones that are 
involved. (1) The target must be insonified: a energy 
must be transmitted into the water and out to the 
target. (2) Some of this energy must be reflected by 
the target. (3) The reflected energy must be trans- 
mitted back to the echo-ranging vessel. (4) The echo 
must be received, amplified electrically, and then 
perceived by the operator. 

The problem can be approached from several 
points of view. The projection of the signal and the 
detection of the echo suggest the immediate impor- 
tance of the equipment. Thus the design of gear 
that will function over long ranges is one aspect of 
the problem. Equally important is the training of 
the operator to utilize the equipment to the fullest 
extent of its possibilities. Thirdly, the transmission 
of sound in the sea must be understood because it 
affects both design and operation of equipment. 
Finally, a foreknowledge of the maximum echo ranges 
for given targets under existing oceanographic con- 
ditions is of importance for tactical reasons, over 
and above the mere operation of the gear; the pre- 
diction of probable maximum ranges thus becomes 
a fourth important aspect of the problem. 

Selecting any one of these points of view would 
lead one to go into detail about some matters and 

a Just as a searchlight illuminates a target, a sound source 
is said to insonify the target. 


to minimize the discussion of others. It is the pur- 
pose, in this book, to consider the problem as a 
whole, in sufficient detail to enable the reader to 
arrive at critical conclusions concerning our knowl- 
edge of it, but not in such detail as to lose perspective. 

Referring to the four steps in the echo-ranging 
process listed above, we can introduce the major 
items that must be examined in a general survey 
of this sort. 

The insonification of the target includes the 
production of the signal and its transmission to the 
target. The production of the signal involves con- 
sideration of the frequency to be used, the power 
output of the transmitting system, and its directiv- 
ity. These three items will form the subject matter 
of the next chapter. The transmission of the 
sound energy to the target was discussed in Part I, 
and thus need enter only incidentally. 

A quantitative discussion of the reflection of the 
sound by the target will involve the concept of target 
strength, introduced in Chapter 5. The numerical 
values of this quantity and the implications for de- 
sign and operation will be discussed in Chapter 8. 

The third process is very similar to the first, 
dealing with the transmission of the reflected sound 
back to the transmitter. 

The fourth process, the perception of the echo, is 
complicated by the fact that the echo must be de- 
tected against a background consisting of airborne 
sounds, noise produced by the echo-ranging vessel 
itself, noise inherent in the sea, and the multitude of 
unwanted echoes called reverberation. This neces- 
sitates the study of methods of portrayal (aural and 
visual) and the design and operation of the receiver; 
moreover, the perception of the echo involves psycho- 
physical factors which must be investigated. Discus- 
sion of these factors will occupy the remainder of 
Part II. 

To sum up, the problems of echo ranging will be 
discussed under the following titles: 

1. “The Acoustic Output of Sonars,” Chapter 7. 

2. “Target Strength and Echo Level,” Chapter 8. 

3. “Maximum Echo Ranges when Background 
Noise is Limiting,” Chapter 9. 

4. “Maximum Echo Ranges when Reverberation 
is Limiting,” Chapter 10. 

5. “Miscellaneous Echo Ranging Applications,” 
Chapter 11. 


133 








Chapter 7 

THE ACOUSTIC OUTPUT OF SONARS 


7.1 IMPEDANCE OF PROJECTORS 

7.1.1 Mechanical Impedance 

P rojectors designed for the generation of super- 
sonic waves in water have a construction that is 
markedly different from that of the familiar loud- 
speakers for the generation of sound in air. It is not 
possible to do justice here to all the factors entering 
into these designs, but some of the basic principles 
are easily summarized. 

The objective, in both cases, is to set the medium 
into periodic motion. To accomplish this, a force 
must be applied to the medium, and this is most 
readily accomplished by means of a plate, or dia- 
phragm, to which the force is applied more or less 
directly. This plate is often a circular disk. Suppose 
it is desired to give a point on its surface the velocity 

v = v 0 cos cot cm/sec, (2) 

where v 0 is the maximum value of the velocity, 
co = 2irf, and / is the frequency of the sound to be 
produced. If this can be accomplished, the water or 
air in immediate contact with the plate will probably 
move with this same velocity. (At least, this will be 
the case if v 0 is not too great. In Section 7.5, the 
possibility will be considered that the medium does 
not follow the motion of the plate, but for the present 
such lost motion will be ignored.) 

* The first problem is the calculation of the force 
required to produce the motion. This force will be 
proportional to v 0 , and to a quantity Z. This is an- 
alogous to the relation between voltage and current 
in an electric circuit, and Z is, by analogy, called 
the mechanical impedance of the plate. The resistance 
and the inductive and capacitive reactances which 
make up the electric impedance have their mechan- 
ical analogies. The value of Z depends on the mass, 
size, and shape of the plate and on its mechanical 
properties, such as stiffness; also on the density of 
the medium, the velocity of sound in the medium, 
and on co. 

The required force will usually not be in phase 
with the velocity. In general, it may be written 

F = v o (X 0 cos cot — Y 0 sin cot) dynes. (3) 


The quantities X 0 and F 0 are called the mechanical 
resistance and reactance, respectively, of the plate. 

The power required to maintain the motion will be 

P 0 = JX 0 i’o 2 ergs/sec = J X 10 _7 X 0 v 0 2 watts. (4) 

In the simplest possible case, that of a perfectly 
rigid plate suspended by light threads in a vacuum, 
the resistance X 0 would be zero, so that no power is 
required to maintain the motion. The reactance Y o 
would be given by 

F 0 = Moo, (5) 

M being the mass of the plate. 

7.1.2 Radiation Impedance 

In practical cases, when the plate is placed in an 
actual medium and supported in a more complicated 
manner, the expression for the impedance becomes 
more complicated. In general, we may write 

X 0 = X + X„ F 0 = F + Y P , (6) 

where X P and Y v are the impedances that would ap- 
ply when the projector is in vacuo, and X and F are 
additional impedances which result from the motion 
imparted to the medium. These added impedances, 
X and F, are called radiation impedances . 

The two forces X cos cot and F sin oot result from 
different processes. The former results from the com- 
pression and rarefaction of the medium, which con- 
stitutes the sound radiated to a distance. The power 
radiated as sound will be given by 

P = J • 10 7 X v 0 2 watts. (7) 

The component F sin cot results from a purely local 
motion of the water in the neighborhood of the plate. 
The energy involved in this motion is not radiated 
to distant points. 

Strictly speaking, while the term radiation resist- 
ance accurately describes the quantity X, the quan- 
tity F should not be called the radiation reactance. 
The ratio F/co is the mass of water that moves back 
and forth with the vibrating projector. If the medium 
were incompressible (infinite velocity of sound), X 
would be zero. The quantity F/co, however, would 
be finite. 


136 


THE ACOUSTIC OUTPUT OF SONARS 


The radiation impedances are more or less in- 
dependent of the mechanical properties of the plate 
but depend on its size and shape, and on the acoustic 
properties of the medium. They may be written 

X = pcSU, Y = pcSV, (8) 

where p = density of the medium (gm/cm 3 ), 

c = velocity of sound in the medium (cm/sec), 
S = area of the plate, 

U,V = quantities to be discussed below. 

It is immediately clear that the radiation imped- 
ance of a given plate will be vastly different in air 
than in water, for the numerical value of the product 
pc is about 150,000 for water and only 42 for air. 
This comes about largely because water is 800 times 
more dense than air; the velocity of sound is also 
nearly five times greater. To cause a given velocity 
of the plate in water will thus require a force which 
is nearly 3,600 times greater than that which would 
cause the same motion in air. Consequently, to cause 
the plate to radiate a given power into water will 
require 60 times the force that would be needed in 
air. Conversely, to radiate a given power into water 
requires only one-sixtieth of the velocity that would 
be needed to accomplish the same thing in air. 

The fact that S, the area of the plate, enters into 
equation (8) will be obvious; it therefore remains to 
discuss the factors U and V. These depend largely 
on the ratio of the size of the plate to the wavelength 
of the sound in the medium, and to a lesser extent 
on the shape and mechanical properties of the plate. 
Figure 1 is a graph of their values for a rigid circular 
plate, as a function of the ratio a = ird/ X, d being the 
diameter of the plate and X the wavelength of the 
sound. 

It is seen that when a is greater than 6 or 7, the 
approximation £7=1, V = 0 is fairly good. On the 
other hand, when a is less than 1, both U and V 
become small. This might be considered a desirable 
circumstance, were it not that U decreases more 
rapidly than V. Thus the power radiated decreases 
more rapidly than the force required: the out-of- 
phase component of the force becomes large com- 
pared to the in-phase component. This is entirely 
analogous to the concept of the power factor in alter- 
nating current theory. A large plate has a high power 
factor, a small plate a very low power factor. In the 
case of supersonic waves, it is fortunately possible to 
make the projector large enough to take advantage 
of this fact, but for low frequencies the dimensions 
required would become prohibitive. Thus, for 1000-c 



Figure 1 . Variation of the quantities U and V, 
equation (8), with a(=ird/\). 


sound, X = 5 ft (approximately), so that even a = 4 
would require d = 6.5 ft. 


7.1.3 The Motor 

The force required to drive the diaphragm or plate 
at the velocity v 0 is supplied by an electromechanical 
device which is called the motor. It is similar to the 
ordinary motor in that it converts electrical power 
into mechanical motion, but, since the motion is 
oscillatory rather than rotatory, the analogy is not 
very close. 

A closer analogy is obtained by considering the 
motor as a transformer. Then the velocity is 
analogous to the output current, and the force F to 
the output voltage of the transformer. The radiation 
impedance is directly analogous to the impedance 
of the output circuit of the transformer. This analogy 
can be used to describe the effect of taking a projector 
out of water and into air. Suppose the projector has 
been designed to work under water. Then the lower 
radiation impedance of air will effectively short- 
circuit it. The projector will heat up, just as an ordi- 
nary transformer when it is short-circuited. Very 
little power will be usefully transformed. 

Conversely, a projector designed to work efficiently 
in air is analogous to a transformer with a low- 
voltage, high-current secondary. It will not be 
efficient under water, where the requirements cor- 
respond to a high-voltage, low-current secondary. 

The physical differences between a loudspeaker 
designed to work into air and a projector designed 
to work into water can be understood by means of 
this analogy. The former always has a thin diaphragm 


MAGNETOSTRICTION PROJECTORS 


137 


of small mass — one that is easily movable. The motor 
usually applies the necessary small force by magnetic 
means. In principle, a small bit of magnetized steel 
attached to the diaphragm might be attracted and 
repelled by a stationary electromagnet through which 
an alternating current is passed. Even if such a de- 
vice could be immersed in water without physical 
damage, the force obtainable in this way would not 
be sufficient to move the mass of water in contact 
with the diaphragm, and it would “stall.” 

Underwater projectors usually (though not always) 
have more massive diaphragms, which are appro- 
priately described as plates. The moving part of the 
motor is in rigid physical contact with the plate. The 
large force necessary to move the plate and adjacent 
water is produced by any of several methods. It is 
possible to design electromagnets to furnish this 
force, but most motors in use at the present time 
depend on the magnetostrictive or the piezoelectric 
effect for this purpose. These effects are capable 
of producing large forces without the complica- 
tions that would result from the use of large elec- 
tromagnets. 


7.2 MAGNETOSTRICTION PROJECTORS 


MAGNETIC FIELD, GAUSS 




7 . 2.1 The Magnetostrictive Effect 

If a rod of a ferromagnetic material is brought into 
a magnetic field parallel to its long axis, the length 
is changed slightly. The change in length is inde- 
pendent of the sign of the field, and may be either a 
decrease or an increase. Its magnitude depends on 
the material, its heat treatment and present tem- 
perature, and on the degree to which it was previously 
magnetized. The effect was discovered by Joule in 
1847 and is called magnetostriction. 1 

The phenomenon is not related in any simple man- 
ner to other magnetic properties. Figure 2 shows the 
relative change in length dL/L, as a function of the 
field strength in gauss, for several elements. It is seen 
that nickel possesses the property of magnetostric- 
tion to a much greater degree than any other, even 
iron. It decreases in length in a fairly regular manner 
for an increasing field strength up to about 200 gauss ; 
if the field is increased beyond this value, the addi- 
tional change becomes extremely small. The extreme 
relative change in length is about 40 parts in a 
million. However, since the Young’s modulus of 


Figure 2. (Top) Magnetostriction in iron, nickel, and 
cobalt. The curves show the relative change in length 
of a rod as a function of the magnetic field strength. 
(Bottom) Construction of a magnetostriction projector 
head. 

nickel is great, a large force is exerted against any- 
thing which resists this small change in length. 

Besides nickel itself, certain of its alloys exhibit 
marked magnetostrictive properties, among others, 
Invar, Monel, and Permendur may be mentioned. 

Magnetostriction is reversible. If a previously 
magnetized rod of nickel is stretched, the magneti- 
zation of the rod is decreased; if it is compressed (in 
the direction of its length), the magnetization is 
increased. 2 

722 The Magnetostriction Oscillator 

Magnetostriction is applied to the production of 
sound waves as follows: a nickel rod is subjected to 
an alternating magnetic field by winding a coil of 
wire around it and sending an alternating current 
through the coil. The rod is shortened periodically 


138 


THE ACOUSTIC OUTPUT OF SONARS 



Figure 3. Quartz crystal, showing X-cut and Y-cut 
plates. 


in response to the changing field. Since the change 
in length is independent of the direction of the field, 
the rod would elongate twice during each cycle of 
the alternating current. This can be prevented by 
suitably premagnetizing the rod, or by sending a 
continuous direct current (a “polarizing current’’) 
through the coil. 

The natural fundamental frequency of vibration 
N of a rod of length L is given by 



where E is the modulus of elasticity and p the density 
of the material. If a current of this frequency is sent 
through the coil, the amplitude of the oscillations 
will be a maximum; relative changes in length may 
be of the order of one in ten thousand. From equation 
(9) -it can be calculated that a rod of nickel 5 in. long 
has a fundamental frequency of vibration of about 
20 kc; and one 1.6 in. long will resonate at 60 kc. By 
using harmonics of a higher order, greater frequencies 
are obtainable, though with a loss in amplitude. 

7.2.3 Production of Sound Waves 

If a nickel rod is set in vibration in the manner 
just described, sound waves will be emitted from 
the end of the rod, with a frequency determined by 
the frequency of the magnetizing current. To obtain 
the maximum possible intensity, a practical projector 


is constructed by embedding the ends of hundreds 
of small nickel-alloy rods or tubes in a steel dia- 
phragm of dimensions which ensure that its resonant 
frequency is the same as that of the rods. Each rod 
is excited by its own coil. 

The activating current is generated by a vacuum- 
tube oscillator, and amplified. 3 The polarizing current, 
as mentioned above, serves to prevent a doubling 
of the frequency of vibration of the rods, but it has a 
second function in addition to this. Starting with 
zero magnetization, the magnetostrictive effect is at 
first very small, but at a certain critical value of the 
magnetic field strength the effect becomes decidedly 
more pronounced (see Figure 2). By using a suitable 
value of the polarizing current, it is possible to work 
on the steep part of the curve. 

Because of the reversibility of the magnetostriction 
effect, it is evident that the projector will also act 
as a receiver. Sound waves impinging on the dia- 
phragm will compress or extend the rods ; correspond- 
ing changes in the magnetization of the rods will 
induce alternating currents in the coils, which after 
amplification can activate some portrayal device. 

7.3 THE PIEZOELECTRIC PROJECTOR 

7.3.i The Piezoelectric Effect 

Some crystals develop electric charges on their 
surfaces when they are subjected to pressure or 
tension. This phenomenon, called the piezoelectric 
effect, was discovered by the brothers Curie in 1880. 5 
The electric charges developed are proportional to 
the force applied to the crystal. They are of opposite 
sign for compressions and tensions. 

The effect is reversible, so that if a piezoelectric 
crystal is placed between two electrodes and a charge 
is applied to the latter, mechanical strains result. 
These set the crystal to vibrating. Since the elastic 
properties of such crystals differ in different direc- 
tions, the vibrations will occur in different ways, 
depending on the orientation of the crystal relative 
to the electrodes. In any case, the natural frequency 
of vibration will be given by an equation similar to 
equation (9), where the value of the elasticity 
modulus will differ for different orientations of the 
crystal. 

Three piezoelectric materials are currently used: 
quartz, Rochelle salt, and ammonium dihydrogen 
phosphate (ADP). Crystals of these substances are 


THE PIEZOELECTRIC PROJECTOR 


139 


shown in Figures 3, 4, and 5, respectively. Quartz 
has the advantage that it is strong and insoluble in 
water, whereas Rochelle salt and ADP are quite 
fragile and soluble. The solubility is a disadvantage 
in all seagoing applications, although it can be 
overcome by observing suitable precautions in the 
design and construction of projectors. On the other 
hand, it is an advantage in that it makes possible 
the production of good artificial crystals in the lab- 




Figure 4 v Rochelle salt crystals, showing Y-cut and 
X-cut plates. 


oratory; whereas quartz crystals must be mined, and 
only a small fraction of those found are large enough 
and perfect enough for acoustic purposes. Quartz has 
an additional disadvantage in that it is very hard 
and more difficult to cut and polish even than glass ; 
while both Rochelle salt and ADP crystals are soft 
enough so that they can be cut with band saws and 
shaped with ordinary metal-working power tools, 
if care is exercised to prevent chipping. 

For piezoelectric applications, plates are cut from 
the whole crystal. A few of the possible ways in which 



Figure 5. Ammonium dihydrogen phosphate (ADP) 
crystals, showing 45-degree Z-cut plate. 


plates can be cut are shown in Figures 3, 4, and 5. 
The designations commonly applied to the plates are 
indicated. 

7.3.2 Quartz Projectors 

The British Asdic utilizes X-cut quartz crystals. 
These are laid flat on a steel plate, as shown in Figure 
6A, arranged in a mosaic so that the plate is ade- 
quately covered. An identical plate (not shown in 
the figure) is then laid on top of the crystals, forming 
a sandwich. The sandwich is made mechanically 
rigid by means of clamps at the edges of the plates. 
Insulating washers make it possible to connect the 
plates to the terminals of the a-c source. 

The deformation of the crystal when the voltage is 
applied is shown in Figure 6 A by the arrows. When 
the potential of the upper face of the crystal is posi- 
tive, the thickness increases. Simultaneously, the 
other two dimensions shrink. The changes which 
occur in the length, width, and thickness are such 
that the volume of the plate remains the same. When 
the potential is reversed, the deformations are in the 
opposite sense. (The two faces of the plate clearly 
are not equivalent, hence care must be taken to ar- 
range all the plates in a mosaic so that they expand 
and contract “in step.”) Since the plate will be com- 
pressed during one half of the cycle of an a-c field, and 
extended the same amount during the other half, it 
will vibrate with the same period as that of the field. 
If this is the natural period of the crystal, the ampli- 
tude of the vibrations will be a maximum. The natural 


THE ACOUSTIC OUTPUT OF SONARS 


140 



Figure 6. (A) Construction of Asdic projector. A 
mosaic of X-cut quartz crystals is laid on a steel plate 
as shown; a second identical steel plate (not shown in 
the figure) is laid on the crystal to form a “sandwich” 
to which the voltage is applied. The Asdic uses the 
“thickness” vibrations of the crystal. The arrows 
indicate the deformation. (B) Mounting of Rochelle 
salt and ADP crystals. The large faces of the crystal 
are covered with metal foil, to which the voltage is 
applied. The crystal is cemented to the heavy backing 
plate. The arrows indicate the deformation of the 
crystal. The longitudinal vibration is the one desired. 

frequency of the thickness vibrations (the ones 
utilized in the Asdic projector) calculated from 
equation (9) is 

285.5 

= ~ kc, (10) 

there t is the thickness of the plate in centimeters. 
However, experiments 6 showed that this relation is 
only approximately true, a because the plates will 
generally execute vibrations in other modes than the 
ones mentioned; moreover, in addition to compres- 
sional vibrations, vibrations due to shear may also 
be present. Such additional vibrations coupled to 
the primary ones will tend to change the primary 
frequency of vibration. 

a A. Hund obtained the following experimental relation: 

287 ±5 

/o = kc. 


7.3.3 Rochelle Salt and ADP Projectors 

The plates of Rochelle salt and ADP crystals are 
mounted so as to utilize the length vibrations instead 
of the thickness vibrations, as shown in Figure 6B. 
The two large faces are coated with a metal foil, and 



Figure 7A. Crystal stack for transducer. 


I 



Figure 7B. Crystal stack for transducer. 


the a-c voltage is applied to the foil. The arrows 
indicate the deformation resulting from the in- 
dicated charge. The crystals are cemented to a 


t 


DIRECTIVITY PATTERNS AND INDICES 


141 





Figure 7D. Exterior of crystal transducers. 

single heavy backing plate; in order to prevent 
short-circuiting, the surface of the backing plate 
must be enameled. 

Many crystals are mounted on a single plate, as 
shown in Figure 7, and the sound is radiated from 
the free ends of the crystals. They are protected from 
the action of sea water by a heavy rubber sheet 
which lies on the free ends. The space between 
backing plate and rubber that is not occupied by 
crystals is filled with carefully purified castor oil. 


Traces of moisture would etch the crystals and 
short-circuit the electric connections; even small air 
bubbles would seriously reduce the efficiency of the 
projector. 

ADP crystals possess certain physical characteris- 
tics that make them superior to Rochelle salt crystals 
as elements in underwater sound projectors, and are 
replacing the latter in standard echo-ranging gear. 
The resonant frequency of the length vibrations of 
the 45-degree cut plates shown in Figure 6 is a func- 
tion both of the length L and width w of the plate; 
it is generally multiplied by the length to form a term 
called the “frequency constant,” which is given by 


JL = 64.7 - (13.6) (-1 kc. (11) 


The piezoelectric effect being reversible, a crystal 
projector acts also as a receiver of sound waves inci- 
dent on the diaphragm. The compression of the crys- 
tals generates corresponding electric currents which, 
after amplification, can activate a portrayal device. 


7.4 DIRECTIVITY PATTERNS AND 

DIRECTIVITY INDICES 

7 . 4.1 Directivity of a Projector 

In order to locate a target effectively by means of 
reflected sound energy, it is obvious that the sound 
must be projected in the form of a narrow beam. This 
is achieved by using a large source as described in 
Section 1.2. 

A large source is one whose linear dimensions are 
several times as great as the wavelength of the sound 
emitted by the source. The significance of the wave- 
length in determining the directivity of a source can 
be seen by considering a simple case. 

A “point” source can be pictured as an extremely 
small sphere contracting and expanding sinusoidally; 
such a source would send out energy equally in all 
directions. Consider two point sources, vibrating in 
phase, each of which produces a pressure p at a dis- 
tant point A. (See Figure 8.) If this point A is on the 
perpendicular bisector of the line joining the two 
sources, the travel time for the respective waves 
from the two sources to the point A is the same; thus 
they will arrive at this point in phase, and the pres- 
sure at A will always be 2 p. Consider, however, a 
point B on the line joining the two sources, at which 



142 


THE ACOUSTIC OUTPUT OF SONARS 




F> 



B 

Figure 8. Diagram illustrating directional effect of 
a two-point source. 


each source again exerts a pressure p. If the two 
sources are a wavelength, X, apart, the waves will ar- 
rive at this point in phase, and the pressure will be 
2 p. This will also be the case if the two sources are 
any whole number of wavelengths apart. But if the 
two sources are an odd number of half wavelengths 
apart, a wave from the more distant source will be 
180 degrees (half a period) behind the wave that left 
the nearer source at the same instant, and the sound 
pressure there will be zero. In this case the two 
sources constitute a directional projector, with a 
maximum output along the normal to the line join- 
ing them and zero output along this line. 



Figure 9. Diagrams illustrating directional effects of a 
two-point source. 


If the two sources are separated by some other 
fraction of a wavelength, the difference in the pres- 
sures at points A and B will depend on the amount 
of this separation. For example, it can be calculated 
that if the separation is X/10, the difference in pres- 


sure at A and B is about 5 per cent ; and the smaller 
the separation of the sources, i.e., the smaller the 
dimensions of the whole source relative to the wave- 
length, the smaller will be the difference in pressure 
between points on the two lines under discussion. 

If the point under observation lies in a direction 
making the angle 0 with the normal to the line joining 
the two sources, as shown in Figure 9, the wave from 
one source will lag behind the one from the other by 
a distance d sin 0, where d is the distance between 
the two sources. The phase lag will then be (2v d/\) 
sin 0. It can be shown that the ratio of the resultant 
pressure p at the point C to the pressure p 0 at the cor- 
responding point A on the normal (0 = 0), is given by 



A graph of this function shows a series of maxima 
and minima as 0 is made to vary through 360 degrees 
(see Figure 10). 

Practical sources of sound can be considered to be 
composed of a number of point sources. By reasoning 
similar to that just used, the pressure at any point 
in the field surrounding the source can be calculated. 
The calculation becomes extremely complicated for 
all but the simplest possible arrangements; however, 
they have been made for several simple geometrical 
configurations and are found in standard works on 
sound. 9 - 10 For purposes of illustration, a few formulas 
are cited: 

1. For a set of n equally spaced point sources 
vibrating in phase with the same amplitude on a 
straight line, the ratio p/p 0 defined above is given by 



2. If the elementary sources are arranged in sur- 
faces, such as the square or rhombus, circle, and 
rectangle, the expressions for p/p Q are different for 
each shape ; but if certain minor approximations are 
made, none of them differs materially from an 
equation similar to equation (13), namely, 


p sin ( ka sin 0) 
Po ka sin 0 


(14) 


where k = 2x/\, and a is the horizontal half-length 
of the projector surface. The square of the ratio p/p Q 
is the function 6(0) defined in Section 1.2. 


DIRECTIVITY PATTERNS AND INDICES 


143 



By substituting values of 0 in equation (14), the 
pressure in all directions relative to the pressure on 
the normal to the surface can be plotted for arbitrary 
values of d and X. If the plotting is done on polar 
graph paper, a directivity pattern results. Such a 
pattern, calculated for a rectangular plate with 
a = 2\, is shown in Figure 5 of Chapter 1. It is found 
that patterns obtained by measurements from actual 
transducers are generally similar to those calculated 
theoretically. 

In order to achieve considerable directivity, the 
linear dimensions of the projector must be several 
times as great as the wavelength of the sound. Sound 
of 10 kc has a wavelength of about 6 in. It is obvious 
that to get directivity at that frequency, or at a 
lower, one, would require a larger projector than for 
the higher supersonic frequencies. 

7.4.2 Directivity Patterns 

It is customary to plot the directivity function 
B(0) = —10 log 6(0) rather than 6(0) itself; by this 
means the importance of the side lobes is stressed, 
as was mentioned in Section 1.2 and as can be seen 
from Figures 6 and 7 of Chapter 1. In echo ranging, 
the side lobes are important because an echo may 
be received along one of them and considered to be 
due to sound from the main lobe; this would result 
in a large bearing error. Thus the suppression of side 
lobes plays an important part in the design of trans- 
ducers. As an example, it has been found that if a 
circular disk is constructed of two concentric rings 
and the inner ring is made to vibrate with greater 
amplitude than the outer one, the first side lobe may 
be as much as 10 to 12 db lower than it would be if 
the diaphragm were a simple circular plate with all 
points on it vibrating with the same amplitude. 


The width of the beam is designated by the angle 
subtended by the main lobe where it is 6 db below 
maximum response. 



Figure 11. Three-dimensional directivity pattern for 
a circular plate. Frequency = 25 kc; diameter of plate 
= 15 in. 


Since the beam itself is three-dimensional, the 
plane in which a directivity pattern is measured must 
be specified. If the projector is a circular piston, the 



144 


THE ACOUSTIC OUTPUT OF SONARS 



Figure 12. Directivity patterns of QGA echo-ranging 
transducer. The solid curve is the pattern for the 15-kc, 
the dotted curve, that of the 30-kc projector. The 
numbers on the axis indicate decibels below the maxi- 
mum. Directivity index: at 15 kc, —18.1 db; at 30 kc, 
-23.2 db. 

beam may have symmetry about the normal to the 
projector face, as illustrated in Figure 11; but if the 
instrument is nonsymmetrical, there exists a direc- 
tivity pattern for each possible axis of rotation, and 
in general these various patterns will be different. 

Theoretically, any desired directivity pattern can 
be obtained by using the appropriate combination 


90 ° 60 ° 30 ® 



Figure 13. Directivity pattern of magnetostriction 
(QC) 24-kc echo-ranging transducer. Numbers on the 
axis indicate decibels below maximum. In this gear the 
tubes are arranged in circular form, and are premag- 
netized by a polarizing current. Directivity index = 
-21.4 db. 

of the shape and dimensions of the diaphragm, spac- 
ing of the sound-generating units, and frequency. 
Practically, any desired pattern can be approxi- 
mated more or less closely by designing a projector 
according to calculations based on the theory. 


Detecting submarines under diverse circumstances 
sets requirements for echo ranging that can be met 
only by using several projectors. For general long- 
range search purposes, it is desirable to have a 
relatively wide beam with circular symmetry and 
small attenuation; for this purpose a circular piston 
driven at, say, 15 kc is suitable. For close ranges, a 
narrower beam could be achieved by using sound 
of 30 kc ; the loss in range due to increased attenua- 
tion at the higher frequency is compensated for by 
the greater concentration of the beam and the greater 
accuracy in obtaining bearings on the target. The 
QGA magnetostriction transducer is designed along 
these lines. The two projectors are mounted in a 
single dome. The directivity patterns for the two 
frequencies of the QGA are shown in Figure 12. 

Directivity patterns of projectors in current use 
are shown in Figures 13 to 17. The type of sound 
generator is designated by a code letter. The QC type 
uses magnetostriction and the QB type the piezo- 
electric effect. Figure 13 shows the pattern of the 
standard QC projector, which consists of 608 hollow 
nickel tubes arranged on a circular diaphragm. In 
this gear the tubes are premagnetized by a polariz- 
ing current. Another form of QC gear, the QCU, has 
the directivity pattern shown in Figure 14. 


60 * 30 * 



Figure 14. Directivity of magnetostriction 25-kc echo- 
ranging transducer (QCU). Rods are spaced in equi- 
lateral triangle; premagnetized by permanent magnets. 
Numbers on axis indicate decibels below maximum. 
Directivity index = —22.5 db. 

This unit consists of 182 nickel tubes spaced in an 
equilateral triangle; the tubes are premagnetized by 
permanent magnets. 

Directivity patterns of two types of QB trans- 
ducers are shown in Figures 15 and 16. Figure 15 is 
the pattern of the QBF, an echo-ranging projector 


DIRECTIVITY PATTERNS AND INDICES 


145 


60 ° 30 ® 



Figure 15. Directivity pattern of Rochelle salt (Y-cut) 
crystal echo-ranging transducer (QBF) at 30 kc. 
Numbers on axis indicate decibels below maximum. 
Directivity index = —25.2 db. 



Figure 16. Directivity patterns of Rochelle salt crystal 
(45° Z-cut) echo-ranging transducer (QBG) taken in 
both the vertical and horizontal planes. Directivity 
index for horizontal pattern at 22.5 kc=— 17.3 db. 
Numbers on axis indicate decibels below maximum. 


consisting of 450 Y-cut Rochelle salt crystals mounted 
on a steel plate. The active area is about 10.5 in. 
square. Figure 16 shows the patterns of the QBG 
projector taken in the horizontal and vertical planes 
at 22 kc. The QBG is a small Rochelle salt gear in- 
tended for small ships. 

Very often a third projector is mounted with the 
QGA system, the function of which is to determine 
the depth of the submarine. One such projector has 
a beam pattern that is fan-shaped, i.e., it is very 
broad in the horizontal plane, whereas in the vertical 
plane the angular width of the beam is only about 
3 degrees. It is a quartz projector driven at 50 kc. 
This transducer is mounted in such a way that it 
can be tilted in the vertical plane as well as rotated 
in the horizontal one. The directivity pattern of 
this transducer is shown in Figure 17. 

When the transducer is used as a hydrophone, the 
directivity pattern is generally found to be nearly 
identical with its pattern when used as a projector, 
provided the electric connections to the acoustic ele- 
ments, i.e., the crystals or the magnetostriction tubes, 
are not altered when the gear is changed from send 
to receive. Hence the directivity function B gives 
information concerning the response of the trans- 
ducer to sounds coming from a specified direction. 
More complicated cases arise, however, in which the 
sources of sound are more or less uniformly dis- 
tributed in all directions. The directivity function 
also gives some information about the response of 
the transducer to such multidirectional sound fields, 
for it is obvious that its response will be largely 
caused by those sources in the direction of the 


principal lobe, and that sources in other directions 
will not contribute appreciably. 

Such sounds are very often unwanted ones that 
interfere with the reception of echoes. It will be 
shown (see Chapter 9) that the interference caused 
by these unwanted sounds is of considerable impor- 


240 * 270 ° 300 ® 330 * 



Figure 17. Directivity pattern, in vertical plane, of 
a quartz projector at 50-kc, used for depth determina- 
tion. Numbers on this denote decibels below maximum. 
The horizontal pattern of this transducer is quite broad. 

tance in echo ranging; thus the response of a sonar 
projector to them, and their previous measurement 
under various sea conditions and at various loca- 
tions, all become important. 

The magnitude of a multidirectional sound field 
is most readily specified in terms of its rms sound 
pressure p. This can be directly measured by means 
of a nondirectional hydrophone, that is, one for 
which b = 1 in every direction. 


146 


THE ACOUSTIC OUTPUT OF SONARS 


The electric connections to the acoustic elements 
of a transducer may be altered when its function is 
changed from projector to receiver for the purpose 
of providing a means for accurate bearing deter- 
mination. One method that is used is to split the 
transducer elements into two halves, and connect 
these in such a way that through one amplifier the 
transducer is most sensitive to sounds coming from 
slightly to the right of the transducer bearing; simul- 
taneously through another amplifier, it is most 
sensitive to sounds coming from slightly to the left. 
The transducer, as a hydrophone, will thus have two 
(possibly different) directivity patterns, and these 
will not be the same as the pattern when the electric 
connections are not altered. This is discussed in 
detail in Section 11.2.3. 

7.4.3 The Directivity Index 

Definition 

The directional characteristic of a transducer could 
be described by stating the fraction of the sound 
energy that is sent out in the desired direction. This 
is done essentially by computing the directivity index. 

Suppose the sound intensity at a fixed distance 
from the projector is measured in a given plane (for 
example, the horizontal plane containing the normal 
to the projector face) in equal angular steps around 
the circle. If the average of all these intensities is 
divided by the maximum intensity, this ratio, called 
the directivity factor K, evidently provides quan- 
titative information on the directivity. For, if this 
ratio is unity, the projector is entirely nondirectional, 
whereas if it is a small fraction, it is evident that a 
large proportion of the energy is concentrated near 
the direction of maximum emission, the “acoustic 
axis.” 

If the average intensity is /, and the maximum or 
axial intensity is la, the directivity index D is de- 
fined by 

D = 10 log K = 10 log — . (15) 

la 

For a nondirectional transducer, D is zero; for a 
directional one, D is a negative number. The direc- 
tivity indices of the various highly directional 
transducers mentioned in the preceding section range 
from — 20 to — 26 db. 


The concept of the directivity index given above 
can be generalized by applying it to three dimensions. 
To do this, it is necessary to find the average value 
of the intensity over a sphere surrounding the pro- 
jector, from the three-dimensional directivity pat- 
tern. This average value depends somewhat on the 
size of the sphere; since in practice one is concerned 
with effects at a great distance, the result should 
apply for this condition, and this will generally be 
the case if the radius of the sphere is considerably 
greater than the longest linear dimension of the 
radiating surface. 

The Calculation of the Directivity Index 

The directivity index for an ideal projector of 
given size and shape can be calculated theoretically 
from the constants of the apparatus, without in- 
volving excessively unwieldy mathematical treat- 
ment if certain simplifying assumptions are made. 
For example, a circular plate whose diameter d is 
greater than two wavelengths can be shown to have 
an index that is given approximately by 

<i6) 

where / is the frequency and c the velocity of the 
sound. 

Generally, D is calculated from the beam pattern, 
or directivity function, b, which was defined by 
equation (14) of Chapter 1: 


1 



where I is the intensity at a given point and I a the 
intensity at a point equally distant from the source, 
but located on the axis. If b is averaged over all di- 
rections, this average evidently gives K and hence D. 

Directivity Index of a Receiver 

When used as a hydrophone, the directivity index 
of a transducer is defined as follows. 

Sound incident on the hydrophone from a standard 
source located at a point in any direction at a dis- 
tance r from the source will generate electrical power 
R. The same source placed on the acoustic axis at 
the same distance will generate electric power R a . 
The ratio R/R a can be called b', the directivity 
function of the receiver. The values of b and b' are 
equal for a given transducer; unless, as was de- 


THE SOUND OUTPUT 


147 


scribed above, the transducer is split for accurate 
bearing determination. 

As in the case of the projector, b' can be averaged 
over the directivity pattern, and the value of D 
calculated as before. 

The directivity index of a hydrophone also deter- 
mines its response to a multidirectional sound source. 
Consider two sound fields, one caused by a single 
source located on the axis of the hydrophone, and 
another by sources distributed equally in all direc- 
tions from the hydrophone. Let both sets of sources 
result in the same sound pressure at the hydrophone, 
and let E a be the electromotive force generated in 
the hydrophone by the single source, E t the emf 
generated by the isotropically distributed sources. 
Thus 

20 log E t = 20 log E a + D. 

Since D is a negative number, E { will be less than 
E a . This relation is of considerable practical im- 
portance. 

7.5 THE SOUND OUTPUT 

7.5.i Electrical Power Input and 

Acoustic Power Output 

A projector is essentially a device for converting 
electric power applied to the system into acoustic 
power in the water. In rating a projector, we are 
interested in knowing how much of the applied 
electric power is available as acoustic power, and 
how much of the available acoustic power is con- 
centrated in a narrow beam. 

The electrical power input can be measured either 
from the open-circuit voltage of the generator and 
the impedance of the circuit, or from the current 
and impedance. 

The acoustical power output can be computed 
from measured pressure levels. The total power is 
given by the energy flow per second over a sphere 
surrounding the projector. The average intensity 7, 
over a sphere of radius r multiplied by the surface 
area of the sphere 4 xr 2 , therefore is a measure of the 
acoustic output of the projector. Since 7 = KI a , 
where K is the directivity factor and I a is the axial 
intensity, the acoustic power is given by 4:Tr 2 KI a . 

The axial intensity is commonly measured by 
mounting a hydrophone at a convenient distance on 


the acoustic axis of the projector, and transmitting 
continuous sound, using a constant current. 

7.5.2 The Efficiency and Response of 
a Projector 

Only that portion of the electric power that is 
converted into acoustic power is available for echo 
ranging. The efficiency of a projector is defined in 
decibels by 10 log ( Po/Pi ), where P 0 is the acoustic 
power output and P t the electric power input. If a 
system is, say, 50 per cent efficient, the efficiency is 
given by 10 log (3^) = — 3 db; an efficiency of 10 per 
cent would be — 10 db, etc. The efficiency of a stand- 
ard echo-ranging projector ranges from — 2 db to 
— 15 db. 

In rating a projector, a convenient method is to 
state the axial sound level reduced to 1 yd b (the axial 
source level) per volt or ampere of the impressed 
voltage or current. This is called the response of 
the projector. 

The acoustic power output P, the axial source 
level S a , and the directivity index D, are related by 
the equation 

S a = 71.6 + 10 log P — D. (17) 

The performance of a given projector is completely 
described by the response, the directivity index, and 
the efficiency. The characteristics of some standard 
echo-ranging transducers are listed in Table 


Table 1 . Characteristics of some standard projectors. 


Code 

Type 

Resonant 

freq. 

(kc) 

D 

Source 
level, Sa 

Eff. 

(db) 

QGA-942 

MS* 

30 

- 23.2 db 

85 db 

-6 

QGA-941 

MS 

15 

-18.1 

77 

-7.5 

QBF 

RS** 

Y-cut 

24 

-21.1 (20 kc) 
- 23.5 (26 kc) 
-25.2 (30 kc) 

88.5 

-3.6 

QBG 

RS 

X-cut 

22 

- 17.3 (22 kc) 

33 (22 kc) 
39 (45 kc) 

? 

QCU 

MS 

25 

-22.5 

84 

-3.8 

QC-L 

MS 

20 

-21.4 

43* 

-9.5 

QC-J 

MS 

24 

-22.1 

46.5* 

-9.5 

Asdic 

Quartz 

15 

-22.0 

56 

-3.1 


* MS = Magnetostriction. 
'* RS = Rochelle salts. 


b The standard unit distance for calibration adopted by the 
Navy is 1 m. One yd and 1 m are not sensibly different in this 
connection. 


148 


THE ACOUSTIC OUTPUT OF SONARS 


7.5.3 Limitation of Power Output by 

Electrical Characteristics 

It would appear from equation (26) that very long 
echo ranges might be achieved by increasing the 
power input into the projector system, and that the 
only limit on the available power would be set by 
the permissible size and weight of the gear. This is 
not the case. There are two limiting factors in de- 
termining the power output, aside from structural 
requirements. 

The first of these factors results from electrical 
characteristics. The voltage across the face of a 
crystal cannot be increased indefinitely, for at a 
certain critical voltage a spark will pass. This is 
referred to as “voltage breakdown.” Some idea of 
the magnitude of the maximum voltage that can be 
applied can be gained from the fact that the speci- 
fications for ADP crystals for echo-ranging trans- 
ducers require that the crystal must withstand a 
resonant-frequency voltage of 20,000 v/in. for at 
least 30 sec. 

In the case of magnetostriction transducers, a 
limitation to the power input is set by the fact that 
the magnetostriction effect becomes negligible when 
a certain critical value of the magnetic field strength 
is reached. Nickel, for example, exhibits practically 
no magnetostriction for field strengths greater than 
200 to 250 gausses (see Figure 2). 

7.5.4 The Limitation of Power Output 

by Cavitation 

The second factor that limits the power output 
of transducers is cavitation. 

An acoustic projector consists essentially of a 
vibrating face or piston. The motion of the face is 
imparted to the water, in which the disturbance is 
propagated as a wave. This process can proceed 
efficiently only as long as the water follows the mo- 
tion of the projector face. When this motion becomes 
too violent, the face tears away from the water, with 
a marked loss of efficiency in the process of sound 
production. 

This limitation on the output of a projector is 
thus closely related to the phenomenon of cavita- 
tion discussed in Section 6.2.2. Let' p be the rms 
acoustic pressure at a point where the normal 
hydrostatic pressure is p 0 . Then once each cycle of 
the sound wave, the total pressure will change from 


Po — 2*p to p 0 + 2 %p and back again. Cavitation 
may occur whenever the total pressure tends to be- 
come negative. Accordingly, the maximum acoustic 
pressure that can be transmitted through a region 
where the hydrostatic pressure is p 0 will be given by 
p = po/2 * or, in terms of sound level, by 
Critical level = 20 log p Q — 3. 

For p 0 = 1 atmosphere = 35 ft of water = 10 6 dynes/ 
cm 2 , L = 117 db. When the sound level exceeds this 
critical value, cavitation bubbles may be formed, 
and cause high transmission losses (see Section 6.2). 
These bubbles have been observed in laboratory 
experiments. 

Since the acoustic pressure is highest at the face of 
the projector, cavitation will occur there before it 
occurs elsewhere. This constitutes the process dis- 
cussed in the first paragraph. As a result of the 
process, the power output of the projector, for a 
given motion of the face, will be reduced. 

Aside from the reduction of power output of a 
projector for a given motion of its face because the 
water does not follow the moving face, the power 
output may also be reduced for other reasons. Thus, 
it has been observed in experimental tanks at Naval 
Research Laboratory, that small air bubbles may 
form on the projector when it is warmer than the 
water. This may also happen under other conditions. 
Accompanying the formation of these almost in- 
visible bubbles, the sound output of the projector, 
for a given electric input, was much reduced. Under 
similar circumstances, its sensitivity as a hydrophone 
also diminished. 

7.6 THE SIGNAL USED IN 

ECHO RANGING 

7.6.i The Signal Frequency 

Practical considerations set rather definite upper 
and lower limits to the frequencies that can be used 
in echo ranging. The use of sonic frequencies (less 
than 10 kc) has not been considered practicable be- 
cause of directivity requirements, as discussed above. 
A second reason for the use of supersonic sound is 
provided by considerations of the detectability of 
echoes. The echo must always be detected against a 
background of interfering noises; while these noises 
include sound of supersonic frequencies, the greater 
part of their energy is in the sonic region. Hence, 
supersonic echoes are masked less than sonic ones. 


THE SIGNAL USED IN ECHO RANGING 


149 


POWER CONTROL UNIT 

RECEIVER UNIT 

RECEIVER TUNING 

BEARING DEVIATION 
INDICATOR 

BEARING INDICATOR 

MASTER VOLUME 

RANGE SELECTOR 



LOUD SPEAKER 


FILTER (PEAK-FLAT) 
SPEAKER VOLUME 
RANGE RECORDER 


TRUE - RELATIVE 
BEARING SWITCH 

SWEEP FREQUENCY 
MODULATOR SWITCH 

I 

HAND KEY 


REVERBERATION 
CONTROL OF GAIN 


TRAINING HANDWHEEL 

HI 

jggggg RECTIFIER 
POWER UNIT 


Figure 18. Model QGB sonar stack. The QGB equipment employs a magnetostriction projector for echo ranging, 
listening, and underwater communication on a supersonic frequency that is between the limits of 17 and 26 kc. ihe 
principal units in the stack are designated on the photograph above. 


150 


THE ACOUSTIC OUTPUT OF SONARS 


An upper limit to the practicable frequency is set 
by the attenuation of the sound in the sea. The 
attenuation coefficient increases very markedly with 
frequency (see Chapter 3, Table 3). Hence, for search 
purposes, where long ranges are required, a frequency 
higher than about 25 to 30 kc is not suitable. When 
the range is being closed, and great accuracy of 
bearing is needed rather than a long range, the 
greater directivity associated with higher frequencies 
is the determining factor, and thus frequencies of 50 
to 100 kc may be found useful. This is especially 
true for depth determination, where an extremely 
narrow beam is required; and since accurate depth 
determination is practicable only at comparatively 
short ranges, the high attenuation consequent upon 
using high frequencies is not significant. 

The U. S. Navy at first adopted a compromise 
value of 24 kc. This frequency allowed fair directivity 
to be achieved while the size of the transducer could 
be kept within practical limits. The attenuation was 
moderate. It is now being replaced by more elaborate 
gear that can emit several frequencies, as mentioned 
above. 

A further reason, of minor importance, for using 
supersonic frequencies is that a high-frequency ping 
is not so readily detected by the enemy unless his 
gear is tuned to the particular frequency used. 

Further investigation may show that the fore- 
going considerations are not conclusive and that 
other frequency ranges merit practical trial. 

7.6.2 Keying Length and Keying Interval 

The best signal duration is a moot question. The 
amount of energy returned to a transducer obviously 
is proportional to the amount of energy sent out; 
hence it would appear that a long signal would pro- 
vide a better chance for a recognizable echo being 
obtained than a shorter one. This is discussed in 
Chapters 8 and 10. Moreover, the signal and echo 
both fluctuate markedly during transmission ; hence, 
a longer signal would provide a greater chance for a 
peak value of the echo strength to be received (see 
Section 3.5). In general practice, signals of a dura- 
tion of about 50 to 200 msec are used. 

A reason for the use of shorter signal duration is 
provided by the fact that the intensity of the rever- 
beration is proportional to the length of the signal 
(Chapter 5), whereas under ordinary circumstances 
the intensity of the echo is not. Consequently, the 


ratio of echo-to-reverberation intensity is greater for 
short signals. This advantage may be canceled be- 
cause aural recognition of the echo is more difficult, 
but shortening of the ping does not affect the 
recognition when a chemical recorder is used. How- 
ever, the echo intensity is independent of signal 
length only if the linear dimension of the target does 
not exceed a certain value. In the case of large tar- 
gets, the echo intensity increases with the signal 
duration. (This will be discussed in more detail in 
Chapters 8 and 10.) 

In sonar gear, the duration of the signal and the 
time interval between signals are controlled at the 
range indicator, a device which enables the operator 
to give the range to the target by noting the position 
on a dial of a flash of light caused by the returning 
echo energy (see Figure 18). One type of indicator 
contains a revolving disk with a slot through which 
the light flashes when the echo energy is received. A 
system of electric motors and gear ratios causes a 
circular disk to complete one revolution either in 1.25 
sec, the approximate time required for sound to 
travel to and from a target 1,000 yd distant, or in 
6.25 sec for a target 5,000 yd distant. The signal 
may be transmitted automatically at the beginning 
of each revolution, or at the beginning of each second 
or third revolution. The time between transmissions 
is called the keying interval. The keying interval is 
usually given in equivalent yards, e.g., if a signal is 
transmitted once for each revolution of the dial, the 
keying interval is expressed as 1,000 or 5,000 yd. A 
nonautomatic, manual keying device is also provided. 

The duration of the signal may be read from the 
scale on the dial; since this is calibrated in yards, it 
is customary to express the ping length in yards in- 
stead of seconds, as has been discussed in Chapter 5. 
If to is the duration of the signal in seconds, the ping 
length P in yards is given by P = 800 1 0 , 800 yd being 
roughly the two-way distance traversed by sound 
in 1 sec. 

7.7 THE EFFECT OF DOMES 

7.7.1 General 

The projector unit, consisting of the projector and 
the shaft that supports it, is usually installed near 
the bow of the ship. Since the housings in which 
projectors are encased are usually spherical, they 


THE EFFECT OF DOMES 


151 




Figure 19C. Standard dome. 

through the stern section of the dome, and the baffle 
also aids in reducing multiple reflection within the 
dome. Some domes are retractable and when not 
in use are withdrawn into a sea chest built into 
the hull. 

Some standard domes are illustrated in Figure 19. 

7.7.2 Acoustic Effects of Domes 

The acoustic effects of the use of domes are two- 
fold. In the first place, it is observed that the axial 
source level of a dome-enclosed projector is less than 
that of the same projector without a dome. In the 
second place, the directivity pattern of the dome- 
enclosed projector differs from that of the same 
projector without a dome. 

The two effects are closely related. It is not possible 
to construct domes of materials that are entirely 
transparent acoustically. Thus, a certain amount of 
multiple reflection occurs inside the dome, as a 
result of which some of the sound energy that is 
emitted by the projector into the main lobe of the 
sound beam is diverted from it. This reduces the 
axial source level. 

Any energy diverted from the main lobe, however, 
must be redistributed in some manner. It is quite 
possible, therefore, that new side lobes may be added 
to the directivity pattern, for the regular shape of 
the dome would preclude a mere random redistri- 
bution of the diverted energy. Moreover, it is obvious 


Figure 19B. Standard dome. 

wanted noise from the propellers. One type is 
equipped with a bulkhead just aft of the projector, 
which supports a sound-absorbing baffle on the for- 
ward side and a sound-reflecting pad on the after 
side; both these devices reduce sound reception 


would cause excessive turbulence, and possibly cavi- 
tation, at even moderate speeds. This would cause 
excessive background noise, as discussed in Chapter 
9. For this reason, transducers are generally enclosed 
in streamlined metal shells called domes. Several 


Figure 19 A. Standard dome. 


types of domes are in current use by the Navy. They 
are all made of corrosion-resistant steel; the front 
is very thin so as to form a “window” to transmit 
the sound; the back is made heavy to damp un- 


152 


THE ACOUSTIC OUTPUT OF SONARS 


that multiple reflections inside the dome may affect 
the original side lobes of the bare projector pattern. 

It can be shown that the decrease in the axial 
source level due to the distortion of the directivity 
pattern is equal to the change in the directivity 
index that ensues when the projector is placed in a 
dome. 


In echo ranging, a loss in the transmission reduces 
the effective range; and the distortion of the direc- 
tivity, especially if accompanied by the formation 
of prominent side lobes, tends to confuse the deter- 
mination of bearings. Hence, the various factors that 
have been adduced must be taken into account when 
designing a dome. 


Chapter 8 

TARGET STRENGTH AND ECHO LEVEL 


8.1 THE CONCEPT OF 
TARGET STRENGTH 

8.1.1 General Principles 

T he study of the echoes received from targets 
obviously constitutes one of the most important 
problems in echo ranging. The theory of echo forma- 
tion has been introduced earlier (see Section 5.2); 
at this time the application of that theory to the 
conditions encountered in practical echo ranging will 
be considered. 

The sound that is scattered by a target is radiated 
by it according to the same laws that describe the 
radiation of sound from primary sources, and which 
were discussed in Chapter 1. As in the case of primary 
sources, we shall find it convenient, when discussing 
echoes, to speak of the source intensity of the in- 
sonified target. This concept, and that of the re- 
radiation itself, can be illustrated very clearly by the 
so-called echo repeater, an artificial target de- 
veloped for the purpose of training personnel. It 
consists of a hydrophone and a projector, mounted 
close together. The hydrophone receives the pings 
from the distant sonar, and its electrical output is 
amplified. This amplified signal is then fed into the 
projector which reradiates it as the “echo.” 

The source intensity of this target is defined as 
the intensity of the reradiated sound at 1 yd from 
the projector on the axis of the latter. Let it be I\. 
If the intensity of the sound incident on the hy- 
drophone is /, the ratio Ii/I would serve to describe 
quantitatively the reflectivity of the target; it might 
be called the overall gain of the repeater. It is more 
usual to convert this ratio to decibels and to call 

T= 10 logy (1) 

the target strength. 

It is found that in order to simulate the echo from 
a submarine, the ratio Ii/I must be of the order of 
magnitude 50 to 100. This gives a general idea of the 
strength of the secondary sources involved in the 
formation of the echoes from a large target, such as a 
ship or submarine. The fact that the ratio h/I is 
greater than unity may seem paradoxical, as im- 


plying that the intensity of the secondary, reradiated 
sound is greater than that of the incident sound; for 
these targets have convex surfaces that cannot focus 
the reflected energy. It must be remembered, how- 
ever, that these targets are large objects: the in- 
tensity of the scattered sound at all actual points in 
front of the target is, of course, less than that of the 
incident sound at the surface of the target; neverthe- 
less, when viewed from a distance, the target radiates 
like a point source concentrated at its center, and the 
strength of this hypothetical point source, given by 
the intensity at a distance of 1 yd, is greater than at 
the surface of the target, several yards distant, where 
the actual intensities of incident and reflected sound 
are equal. This phenomenon is precisely analogous to 
the radiation of sound from large primary sources, as 
discussed in Section 1.2 and illustrated in Figure 
5 of Chapter 1. 

The concept of target strength applies not only 
to the echo repeater, but to any target. In Section 
5.2, it was shown that the intensity of the scattered 
sound I s at a distance r from a target, is given by 
equation (7), 


I (T 



where <r is its target area. If we set r = 1 in this equa- 
tion, we get 



whence the definition of target strength given in 
equation (1) yields 

T = 10 log ^ = 10 log (£\. (2) 


8.1.2 The Target Strength of Spheres 

The concept of target strength, as presented in the 
foregoing, has been experimentally tested. The 
simplest case of reflection is provided by a sphere. 
In this case it is clear that the target area <r, and 
therefore the target strength T, does not depend on 
the direction of the incident sound ; and it was shown, 
moreover, that it is also independent of the direction 


153 


154 


TARGET STRENGTH AND ECHO LEVEL 


of the reflected sound (see Appendix, Chapter 5). 
The target area of a large sphere (Section 5.2) is 
ird 2 / 4, where d is the diameter of the sphere; hence 
its target strength is given by 

l a \ d 2 

= 20 log f '^) db. (3) 

The target strength of spheres as a function of the 
diameter is shown in Figure 1 . 

Optical experiments carried out at MIT show that 
equation (3) does represent the target strength of 
spheres for visible light. 1 - 2 - 3 The intensity of the 

d,YD 

0.1 Q2 03 05 10 2.0 3.0 5.0 10 20 30 50 100 



Figure 1 . Graph of equation (3) for the target strength 
of a sphere whose circumference is greater than ten 
wavelengths of the sound. For smaller spheres, consult 
Section 5.1. 

light reflected by spheres of various sizes from 2 to 25 
in. in diam. was measured at a point near the source. 
All the experimental conditions with regard to the 
projection, transmission, and reception of the light 
were the same for all the spheres; moreover, the sur- 
faces of the different spheres were alike. Hence, the 
variation in intensity could be a function only of the 
size of the sphere. It was found that the level U of 
the reflected light, in decibels above the intensity of 
the reflected light from a sphere of arbitrary diame- 
ter, was given by 

L' = 20 log d + constant. 

The numerical value of the constant could not be 
determined. 

While there is an analogy between the reflection of 
light and that of sound, it is desirable to check the 
theoretical formula by acoustic experiments. Un- 
fortunately, these are difficult to make with the nec- 
essary accuracy. Perhaps the most instructive series 


of experiments was carried out at a calibration sta- 
tion. 4 The separation between the sonar and the 
target was only 11.5 ft. The targets consisted of 
metal spheres 3 ft in diameter. Several different 
spheres were used ; one was constructed of gores welded 
together, the others had a smoother construction, 
but all showed appreciable departures from geometric 
perfection. Various frequencies of sound were used, 
to test the theoretical conclusion that target strength 
should not depend on frequency, provided only that 
the radius of the target is great compared to the 
wavelength of the sound. The results are shown in 
Table 1 ; the theoretical target strength is T — — 12 
db in each case. 


Table 1 . Target strengths of spheres. 


Frequency 

(kc) 

3-ft mine 
case, water- 
filled 

(T db) 

3-ft mine 
case, 
loaded 

(T db) 

33-in. sphere, 
gored con- 
struction, 
water-filled 
(T db) 

3-ft sphere, 
badly dent- 
ed, water- 
filled 
(T db) 

30 


- 10.8 



40 

- 6.9 

- 7.9 

-5.2 

-8.5 

50 

- 6.7 

- 6.0 



60 

- 8.2 

- 7.2 

-3.2 

-9.7 

70 

- 8.4 

- 7.7 



80 

-10.3 

-10.3 

-5.1 


90 

-11.9 

- 8.9 

-3.5 



The observed values are in general considerably 
higher than — 12 db, and the differences are not the 
same for all frequencies. However, there is no sys- 
tematic dependence, and some of the variability is 
doubtless due to experimental error. 

In order to investigate the sources of error, the 
echo intensity was recorded continuously while the 
sphere was rotated. The results are shown in Figures 
2 and 3 for the dented sphere and the water-filled 
mine case. It is seen that a very considerable varia- 
tion results from the departures of the target from 
the ideal geometrical shape. This is emphasized by 
Figure 4, obtained with the gored sphere. 

The general conclusion is that the theoretical 
formula may be used to estimate the target strength 
of a sphere, but that appreciable departures from 
theory may be expected in practice. 

8.1.3 Echo Level 

In most of the previous discussion of echo forma- 
tion it has been tacitly assumed that the transmis- 
sion loss is described by the inverse square law. This 


THE CONCEPT OF TARGET STRENGTH 


155 


270 



Figure 2. Echo from a sphere with large dents, diam. 3 ft. The echo level was recorded continuously while the sphere 
was rotated through two complete revolutions at a depth of 13 ft. Distance from projector to center of sphere = 11.5 ft. 
Pressure level of incident sound at front of sphere =45.7 db. Frequency, 40 kc. 4 



156 


TARGET STRENGTH AND ECHO LEVEL 


270 ' 



180 


Figure 3. Echo from a mine case (water-filled), diam. 3 ft. Experimental procedure and conditions were the same as 
for Figure 2. 4 



157 


% 


THE CONCEPT OF TARGET STRENGTH 


0 ° 



Figure 4. Echo from a gored sphere, diam. 3 ft. Experimental conditions and procedure were the same as for Figure 2. 4 




158 


TARGET STRENGTH AND ECHO LEVEL 


is almost never true at sea, thus it is necessary to 
derive formulas that describe the general case. 

Consider the case of a signal projected by a sonar 
that has a source level S db. In going to the target, 
the sound level of the signal will be reduced H db; 
the value of the transmission loss H depends on the 
range to the target. At the target, the level of the 
incident sound will thus be 

L = S-H db. (4) 

If the intensity of the sound at the target is 7, then 
L = 10 log 7. (5) 

Under the influence of this sound, the target becomes 
a secondary source of sound; the intensity, I h of 
the reradiated sound at the standard distance of 
1 yd is, according to equation (7) of Chapter 5, 



where a is the target area. Taking logarithms of this 
expression, we obtain as the secondary source level 

Si = 10 log Ii = 10 log 7+10 log — , 


where T is the target strength. 

Since, from equation (4), L = S — H, 

Si = S — H + T. (7) 

As this reradiated sound (the echo) travels back to 
the sonar, its sound level is again reduced H db, 
hence the level of the echo at the sonar, denoted by 
E, will be given by 

E = Si-H, (8) 

and, using equation (7), 

E = S-\- T — 2H. (9) 

In this equation E = the echo level, 

S = the source level of the sonar, 

T = the target strength, 

H = the transmission loss from 
sonar to target. 

These four quantities are in decibel units. 

Equation (9) is fundamental to all considerations 
of echo ranging. It may be given another form, since 

H = A + 20 log r, 


(see Chapter 1) where A is the transmission anomaly, 
equation (9) may be written 

E = $-f T — 2A — 40 log r, (10) 

where r now is the range to the target. 

It is to be noted that if the target strength de- 
pends on the aspect of the target, that value of T 
appropriate to the situation is to be used in this 
equation. 

8i4 The Measurement of 

Target Strength 

The discussion up to this point has implied that 
the target strength of a given reflector is a character- 
istic of the reflector, determined entirely by the 
physical properties of the latter — its size, shape, the 
nature of its surface, and its orientation relative to 
the direction of the incident sound. It is necessary to 
investigate the effects of these properties, as well as 
those of the signal, such as its frequency and ping 
length. Three major methods have been adopted in 
this work. 

1. Formulas for the target strength of practical 
targets — for example, submarines — can be derived 
by mathematical methods similar to that illustrated 
in the derivation of equation (3). The calculations 
are complicated and subject to the same uncertainty 
that has already been noted in the case of the 
spherical target. 

2. A convenient laboratory method for measuring 
target strengths of practical targets is provided by 
constructing accurate small-scale models, and com- 
paring the intensity of the echo with the intensity of 
echoes from spheres. The target strength can then be 
expressed in terms of a standard sphere. Visible light 
and high-frequency sound have both been used in 
such model studies. They will be described in Sec- 
tion 8.2. 

3. The most direct and straightforward method of 
obtaining target strengths obviously is to echo range 
on the actual targets in the ocean and to study the 
recorded echoes. The complications introduced by 
working in a medium as variable and unpredictable 
as the ocean make it difficult to interpret the results 
of such measurements. A program of considerable 
magnitude has been inaugurated and partially com- 
pleted in order to obtain and analyze a sufficiently 
large mass of data to warrant definite conclusions 
concerning the design and operation of gear and the 


MEASUREMENT OF TARGET STRENGTH 


159 


construction of submarines. The results of these 
studies up to the time of writing will be summarized 
in Section 8.4. 

8.2 MEASUREMENT OF TARGET 
STRENGTH USING SCALE MODELS 

The specific objectives of the experiments with 
models are: 

1. To determine the target strength as a function 
of the orientation of the target with respect to the 
echo-ranging beam. The orientation is conveniently 
described in terms of aspect and altitude angles, 
defined in Figure 5. In this figure the center of a sub- 
marine is shown as the origin of a system of rectangular 


Y 



Figure 5. Diagram illustrating target aspect and alti- 
tude angles. 

coordinates. The aspect is given by the angle between 
the x axis and the projection of the beam on the 
x-z plane, measured clockwise in degrees from the 
bow of the submarine. Thus, bow aspect is 0 degrees, 
stern aspect 180 degrees, starboard beam aspect 90 
degrees and port beam aspect 270 degrees. The 
altitude of the target is defined as the angle in degrees 
between the echo-ranging beam and the x-z plane. 
This angle is positive if the projector is above the 
target and negative if it is below. Thus, if target 
and projector are the same level, the altitude is 0 
degrees; if the projector is directly above the target, 
the altitude is 90 degrees. 

2. To determine which portions of a vessel are 
mainly responsible for the production of echoes. 


8 . 2.1 Optical Experiments 

Method of Determining the Target Strength 

A series of experiments was carried out at MIT 
in which the target strengths of several classes of 
submarines were determined by optical methods. 1 2 3 
In general terms, the experimental technique was 
to project light onto the models at different aspects 
and altitudes and to receive the reflected light by a 
photoelectric cell located near the source. The re- 
sulting electric current was amplified and measured. 
The models were then replaced by spheres of various 
sizes (see Section 8.1.2) and the intensity of the 
light reflected by them measured in the same manner. 

The target strength of the submarine represented 
by a given model was calculated as follows: 

From equation (9), the target strength of the 
model T' is 

V = e'-S+2H, 

where E f is the intensity level of the reflected light 
in decibels above some arbitrary reference, dictated 
by considerations of convenience in using the ap- 
paratus. The source level S will, of course, also be in 
decibels above the same reference level as E f . The 
target strength T 0 of a comparison sphere substi- 
tuted for the model, is 

To = E 0 -S+2H, 

where E 0 and S are referred to the same zero level 
as before. If proper precautions are observed, S and 
H will be equal in both measurements; hence 

T f - T 0 = E' - E 0 db. 

If the comparison sphere duplicates the echo level 
of the model, E' = E 0 and T' = T 0 , and the target 
strength of the model then is given by equation (3), 

T' = 20 log d 0 — 12 db, 

where d Q is the diameter of the equivalent sphere. 
To obtain the target strength of the actual submarine, 
d 0 is multiplied by the scale factor, k, of the model; 
whence finally 

T — 20 log (kdo) — 12 db. 
Experimental Results 

Some typical results of the measurements de- 
scribed above are exhibited in Figures 6 to 8. Figure 
6 shows the reflection from a model of a submarine 
of the S class. It is evident that echoes from aspects 


160 


TARGET STRENGTH AND ECHO LEVEL 


other than off the beam are negligible compared with siderably less than for 0 degrees altitude, but the 
the latter; for at aspects more than 30 degrees re- general pattern of the curves is similar at all altitudes, 
moved from beam aspect the target strength is nearly 
20 db less than the maximum. 

Criticism 


90 ° 



Figure 6. Target strength of a submarine (S class) 
model measured by optical method, showing variation 
with aspect. Points show averages of both sides of the 
model. Zero altitude. 2 


90 * 



Figure 7. Target strength of model submarine of 
Figure 6 by optical method. 2 Altitude = —45 degrees. 


90 ° 



Figure 8. Target strength of submarine model of 
Figure 6 by optical method. 2 Altitude = +10 degrees. 


The effect of altitude is shown in Figure 7 and 
Figure 8, which show the reflectivity from the same 
model at an altitude of — 45 degrees and + 10 degrees, 
respectively. The target strength is seen to be con- 


The chief criticism of optical experiments on 
models is based on the fact that the wavelength of 
the light used is not properly scaled. For example, 
if a scale factor of 60:1 is used in constructing the 
model, the wavelength of the light corresponding to 
the wavelength of 24-kc sound would be 1 mm. This 
is in the far infrared or ultrashort microwave region, 
and is not practicable for these experiments. As a 
consequence of the wrong wavelength, the results 
may be in error because of the effects connected with 
the diffraction and nonspecular reflection of the 
sound. The chief consequence of these errors is that 
the effect of the conning tower may be overempha- 
sized and that of the bow and stern reduced too 
much. 

An additional handicap in experiments with light is 
provided by the fact that the effects of inaccuracies 
in the construction of models are exaggerated. More- 
over, it is not possible to reproduce all the ship’s 
fittings in the model, and these may possibly be 
important. In this connection also the diffuse re- 
flection caused by minor irregularities must be consid- 
ered; in the experiments these effects were minimized 
by using glossy surfaces. For all these reasons it is 
possible that target strengths of submarines estimated 
from models may sometimes be in error by as much 
as 10 db. 

One objection has been raised, based on the as- 
sumption that if a submarine is in motion, its hull is 
surrounded by a blanket of turbulent water, and 
perhaps of air bubbles, the effect of which may be to 
alter the reflectivity considerably. However, there is 
little experimental evidence to support this assump- 
tion of an appreciable acoustic effect of the turbulent 
blanket surrounding the submarine. It is known, 
however, that the wakes of both surface vessels and 
submarines can be detected by echo ranging (see 
Chapter 6). 

Photographic Studies 

In connection with the experiments just described, 
the reflected light could also be admitted to a camera, 
in the expectation that the resulting photographs 
would give clues as to the most likely areas of sub- 
marines that produce strong echoes. Such photo- 



MEASUREMENT OF TARGET STRENGTHS OF SHIPS, SUBMARINES 


161 


graphic studies were also carried out at San Diego. 5 
At the latter laboratory, a model HMS Graph , 
finished with glossy white enamel, was photographed 
from various aspects (see Figure 9). The model was 
then covered in part by vertical and horizontal cor- 



Figure 9. Photograph of Model of HMS Graph , 
beam aspect. The model was finished with glossy 
white enamel. 



Figure 10. Similar to Figure 9, except that vertical 
and horizontal corrugations were attached. 



Figure 11. Similar to Figure 9, with parts of the model 
covered by emery cloth. 


rugations (Figure 10) and by emery cloth (Figure 
11), with the objective of reducing prominent re- 
flections. 

8.2.2 Acoustic Experiments 

The inaccuracies associated with the wrong scale 
factor of the light used in the optical experiments 
just described were avoided in another study of 
target strengths by using ultrasonic sound. 6 A model 
of HMS Graph , built to a scale of 1:60, was sus- 
pended in water, and continuous sound of 1,565 kc 
was projected against it. This frequency corresponds 
to echo ranging on the actual submarine at 26 kc. 
The echo level was measured for all aspects of the 
model at distances ranging from 1 to 17 ft, corres- 
ponding to actual target ranges between 20 and 340 
yd. The target strength of the model T M was calcu- 
lated by using equation (9), 

T m = E-S + 2H. 


The transmission loss was assumed to be 
H = 20 log r. 

The value of T M was increased by 20 log 60 (the 
scale factor of the model) to obtain the target strength 
of the actual submarine. 

The target strength, for all aspects, measured in 
this manner is shown in Figure 12; the curve is the 
average of the two sides of the model. The target 


90 * 



TARCET STRENGTH, DB 


Figure 12. Target strength of submarine model of 
Figures 9 to 11, measured in water with 1,565-kc sound. 
Echo level measured at distances of 1 ft to 17 ft. The 
curve is the average of the two sets of experimental 
points. 

strength decreases nearly 20 db from its value at 
beam aspect for aspects more than 20 degrees from 
the beam. Bow and stern aspects show greater target 
strength than the corresponding optical measure- 
ments indicate. 

Experiments with models are valuable in that they 
give the order of magnitude, at least, of the target 
strengths of practical targets; but the great scatter 
of the observed points indicates the difficulty of ob- 
taining precise results. 

8 3 MEASUREMENT OF THE TARGET 
STRENGTHS OF SHIPS AND SUBMARINES 

8 . 3.1 General Considerations 

All measurements in echo ranging are based on the 
fundamental equation (9), 

E = S+T-2H, 

whence the target strength is given by 

T = E-S+2H. (11) 

This equation involves four quantities. If the echo 
level E, the source level S, and the transmission H 






162 


TARGET STRENGTH AND ECHO LEVEL 


could all be measured while echo ranging on an actual 
ship or submarine, the target strength of T of the 
latter could be calculated. 

The primary difficulty is that these three inde- 
pendent measurements must all be made at sea. It 
has been seen that such measurements are rendered 
difficult by the extreme variability of the ocean. 
Consequently, each of the three measurements will 
be subject to errors of considerable magnitude, and 
the computed value of the target strength will be less 
accurate than the least accurate of the three measure- 
ments involved. 

In addition, secondary difficulties are encountered 
in the work because of the problems of seamanship 
and navigation that arise when a surface vessel and 
submarine are required to execute precise maneuvers 
together. 

The accuracy might possibly be improved by using 
the method of comparison spheres, as described 
above in the discussion of the optical experiments; 
this would reduce the required measurements to 
determinations of echo levels alone, since S and H 
would cancel out. However, the problem of handling 
large spheres at sea is so difficult that this method has 
not been used to any extent. 

In the following, some attention will be devoted to 
the measurement of the three quantities, and to pro- 
posed means for surmounting or avoiding the dif- 
ficulties. 


832 The Measurement of E— S 

In principle, S could be determined by measuring 
the electric input during transmission, the sonar 
being calibrated to give the equivalent source level. 
If V s is the electric input of the signal, and K P the 
calibration constant of the sonar as a projector, 

S=Vs + K P . (12) 

All these quantities are in decibel units. Similarly, 
the echo level E would be determined from 

E = V e-\~ K h , (13) 

where V e is the electric output during the reception 
of the signal, and K H the calibration constant of the 
sonar as a hydrophone. Then 

E - S = V E - V s + K e - K s . (14) 
Of these four quantities, V E and V s can be 
determined quite accurately; at any rate, errors in 
their measurement are negligible compared with 
those in the determination of K E and K s . These 


constants cannot be determined more accurately 
than within ± 2 db even under the best conditions. 
Moreover, their values change from day to day in an 
unpredictable manner; changes in temperature and 
humidity, the growth of fouling organisms on the 
transducer, all contribute to these changes. It is 
optimistic to suppose that they are both known 
within ± 4 db, and consequently, errors in the val- 
ue of E — S will be of the order of + 6 db. This simple 
method of determining E — S is, therefore, far from 
precise. It has been used in most of the experimental 
work, but more elaborate methods have been devised 
in order to eliminate the errors in the calibration 
constants. 

The objective of these more complicated methods 
is, in each case, to obtain an expression for E — S that 
does not involve the calibration constant of any of 
the apparatus used. They all require additional 
equipment and make the operations at sea still more 
difficult. As a consequence, none of them has as yet 
been used extensively. 

An example will be presented to show how it is 
possible to attain this objective. It is the simplest 
of the various methods proposed, but is not the best 
in practice. 

Suppose that, instead of using the same transducer 
both for transmitting the signal and receiving the 
echo, two separate transducers are used for the two 
purposes. They are mounted on separate shafts and 
have separate electric circuits. The values of S and 
E will still be given by equations (12) and (13) when 
these are applied to the appropriate transducer. An 
auxiliary experiment is also performed as nearly 
simultaneously with the echo ranging operation as 
possible. This experiment can be more easily de- 
scribed with reference to Figure 13A. The two sonars 
are trained so that they face each other; Sonar I 
serves as the projector, and Sonar II as the receiver 
of the signal. Sonar I is excited with the input Vs, 
and a signal of source level S is transmitted. This 
signal will travel directly to the hydrophone of Sonar 
II, where its level will be given by 

L = S — H 0 , 

H 0 being the transmission loss over the path separat- 
ing the two transducers. If the electric output of the 
signal at the hydrophone of Sonar II is V' s , and the 
calibration constant is K H , we have, since 

L = V' s -\-K h , 

V's = L — K h = S — H 0 — K h , 
or S = V's~\rHo-\- Kh- (15) 


MEASUREMENT OF TARGET STRENGTHS OF SHIPS, SUBMARINES 


163 



l 10 100 1000 10,000 



Figure 13. Arrangement for eliminating the calibra- 
tion constants of the sonar in determining E — S. (Top) 
Experimental setup. Sonar I and Sonar II are both 
mounted on the echo-ranging ship but on separate 
shafts, facing each other. They have separate electrical 
circuits. ( Bottom ) Schematic of oscillograph record show- 
ing how E — S may be read from the record if H 0 is 
known. S = source level of transmitted signal. 2? = echo 
level. L = sound level of signal at Sonar II. y's = elec- 
trical output of the signal at Sonar II. Vp = electrical 
output of Sonar II during reception of the signal. 

K H = calibration constant of Sonar II as hydrophone. 

An echo received by Sonar II will have an electric 
output V E at its hydrophone, and combining equa- 
tions (13) and (15), we have finally, 

E-S=Ve-V's-H 0 , (16) 

an expression that is independent of both Kh and 
K P , but does depend on H 0 . Figure 13B shows 
schematically how the value of E — S may be read 
from a record if H 0 is known. 

The advantage of this method results from the 
fact that the transmission loss H G is not subject to 
the same erratic changes that bedevil the calibration 
constants. Any error in its determination is thus 
common to all measurements with the same appara- 
tus. Differences in E — S from one set of experimental 
conditions to another, or from one target to another, 
should thus be more accurately determinable than 


by the simple method of measuring E and S inde- 
pendently on the same sonar. 

The method has the practical disadvantage of 
requiring two nearly complete sonar installations on 
the same ship, and this has contributed to prevent- 
ing its use. Analogous methods, more complicated 
on paper but simpler in practical application, have 
been used in a few instances. 


8 3 3 The Measurement of H 

In much of the work on target strengths, the 
transmission loss H experienced by the signal in 
traveling to the target could only be estimated, the 
calculation taking into account the known thermal 
conditions of the sea, and the other oceanographic 
factors that enter into the problem. This method 
results in large errors, and in equation (11) these 
are multiplied by 2; when these are combined with 
the already large error in E — S, the resulting error 
in the value of T is rendered very large indeed. 

The alternative is to measure the transmission loss 
directly. This can be done by making transmission 
runs immediately before or after an echo-ranging 
run. This has been done in some experiments. How- 
ever, it has been observed that the transmission loss 
may change very appreciably even in a half hour, so 
that the method is not too successful. Moreover, it 
has usually been necessary to use a vessel other than 
the target for the transmission run, thus necessitat- 
ing maneuvers by three vessels. 

The obvious way of avoiding both disadvantages 
is to equip the target with a receiver system supplied 
with a recorder. Thus it is possible to measure the 
transmission loss simultaneously with the measure- 
ment of E — S. This has been done in a few cases. 
The chief cause of error in this method is found in 
the difficulties of ensuring that only the direct signal, 
and no reflections from the target itself are picked 
up by the receiver. This technique is being perfected 
at present. 


8 3 4 Errors Caused by Fluctuation 

Even if all the sources of error discussed above 
could be eliminated, one other source would still re- 
main. The echo level depends on the transmission 
loss [equation (9)], and since this quantity fluctuates 
from ping to ping (see Chapter 3), it is to be expected 



164 


TARGET STRENGTH AND ECHO LEVEL 


that the same will be true of the echo. Figure 14 shows 
how widely two successive echoes may differ in level. 

It might be supposed that by making a simultane- 
ous transmission measurement the error due to the 
echo fluctuation could be eliminated. For, since there 



Figure 14. Oscillograms of two successive echoes, 
showing how the echo level may fluctuate from one 
echo to the next. 


PERCENTAGE OF T EXCEEDING STATED VALUES 

qi I 5 20 40 60 80 95 99.9 




• 










































AS 

PECT 

135* 





• 
















Figure 15. Cumulative distribution of target strength 
T of a submarine at constant range. The median value 
is indicated by a short horizontal line, the quartiles by 
short vertical lines, crossing the graph. 


random error of some ± 3 db, while errors of ± 6 db 
occur with noticeable frequency. 

The knowledge of the target strength of submarine 
and surface vessels is fundamental to all sonar de- 
sign and development problems. It is therefore most 
unfortunate that the accurate measurement of this 
parameter should be so difficult. The discussion of 
the sources of error that has been presented here is 
by no means exhaustive, but may serve as an intro- 
duction to an important series of unsolved problems 
in sonar research. 


is only a short time interval between the transmission 
of the ping and the reception of the echo, one might 
assume that the echo level and transmission loss 
would fluctuate together, or, in other words, that the 
difference E — 2 H would not fluctuate. Unfortu- 
nately, the time interval is generally not short enough 
to justify this assumption. Even at a range of only 
400 yd, it is 0.5 sec. Reference to Figure 52 of Chap- 
ter 3 shows that quite large changes in transmission 
loss occur in an interval of this magnitude. Hence the 
transmission measurement cannot predict reliably 
how the sound level will fluctuate on the return trip 
from target to sonar, and it is quite probable that 
the echo level E will fluctuate as much or even more 
than the transmission loss. 

In practice, some attempt is made to eliminate the 
fluctuation by averaging sets of five successive echo 
level measurements. Even with this precaution, the 
values of T, calculated from the average of such sets 
of five echoes, still fluctuate. An idea of the magni- 
tude of this fluctuation is afforded by Figure 15, 
which shows that the values are still subject to a 


8.4 RESULTS OF EXPERIMENTS AT SEA 

8 4i Target Strength as Function of 
Aspect 

The dependence of target strength on aspect is 
shown in Figure 16, which exhibits the results of an 
experiment on a fleet-type submarine, and is typical 
of the experiments of this kind carried out at San 
Diego. The target vessel ran at about 2 3^ knots 
submerged at periscope depth ; the echo-ranging ves- 
sel circled the submarine twice, maintaining a dis- 
tance of about 500 yd. The transmission loss H was 
calculated from the relation 

H = 20 log r + A, 

and the anomaly A was assumed to be 0.005 db/yd 
of sound travel. The value of T was computed using 
equation (13). Each point on the curve is the average 
of all echo observations with the 15-degree sector 
centered at the point and represents the average of 
about 40 echoes. 




RESULTS OF EXPERIMENTS AT SEA 


165 


000 ° 



Figure 16. Dependence of target strength T of a fleet- 
type submarine on aspect angle. 


It is seen from the figure that the variation with 
aspect of the target strength measured in this way 
corresponds roughly to the results obtained by using 
models. One would not expect a very close corres- 
pondence, as there is great variation not only be- 
tween different classes of submarines, but also 
between individual submarines of a given class. This 
can be seen from Table 2, which exhibits the results 


Table 2. Target strength of submarines for various 
aspects (15-degree sectors, 24-kc sound). 


Type of submarine 

Bow 

(db) 

Stern 

(db) 

Abeam 

(db) 

Fleet 

10 

18 

27 

S class 




A 



18 

B 

15 

10 

21 

C 

5 

10 

8 

D 

1 

2 

5 

C (repeated 3 months later) 

2 


14 

E 



22 

B (repeated 8 months later) 


12 (135° aspect) 


Average for all S boats 

6 

7 

15 


of many experiments carried out at San Diego. All 
these measurements were made with 30-msec signals 
of 24-kc sound. 

A systematic dependence of target strength on the 
class of the ship has not been definitely established, 
although the above table suggests that the larger 
fleet-class submarine has a higher target strength, as 
was to be expected. 

Other measurements made at various places and 
times indicate higher values for S-type submarines. 


No explanation for this has been offered. The target 
strengths as measured by model experiments are a 
few db higher for beam aspects, and slightly lower 
for bow and stern aspects, than the corresponding 
values from direct measurements. 


Altitude Angle 

In operational practice the variation of target 
strength with altitude is not significant, since the 
altitude angle is generally quite small. There is 
practically no experimental evidence of an altitude 
effect in echo ranging. 




B. BOW ASPECT 



Figure 17. Echoes from submarines at various aspects, 
using long and short pings. The upper oscillogram of 
each pair is the record of a ping of 26.5-yd length, the 
lower one of a 4.0-yd ping. As the ping length is de- 
creased, the separate echoes tend to become discrete. 


8 4 2 The Form of the Echo as a 
Function of Target Aspect and Ping Length 

A submarine must be considered as an aggregate 
of various targets, rather than as a single one: the 
secondary sources that cause the echo are hot all at 




166 


TARGET STRENGTH AND ECHO LEVEL 


0.4-YD 

PING ECHO 








80-YD PING ECHO 



Figure 18. Oscillograms of echoes of pings of various ping lengths from a submarine presenting beam aspect. The 
records are more extended than those of Figure 17. Each of the first three sets shows three echoes received within a 
period of ten seconds. The echoes are seen to show the effects of interference between the component parts of the echo. 
(Compare with Figure 52, Chapter 3. The original oscillograms were retouched slightly to bring out the outlines of the 
echoes; it is not believed that the form has been changed. 

the same place. This is clearly illustrated by the 
photographs of the model submarines shown in 
Figures 9 to 1 1 ; in practice the number of component 
sources is probably increased by various fittings on 
the deck and hull. Each of these returns its own 
echo; thus it is not strictly correct to speak of an 
echo from a submarine. If the range to the various 
sources is different, each echo will be received at a 
different time. 


With long pings, these separate echoes overlap in 
time and result in a single burst of sound, the en- 
velope of which is very irregular. If the ping length 
is very short, the individual echoes can be distin- 
guished on the oscillogram. This is illustrated by 
Figure 17 : the upper oscillogram of each pair is the 
record of a ping of 26.5-yd length, the lower one of a 
4.0-yd ping. As the ping length is decreased, the 
separate echoes tend to become discrete. This is 











RESULTS OF EXPERIMENTS AT SEA 


167 


more strikingly evident in Figure 18, in which are 
shown oscillograms of echoes recorded with the 
camera speeded up, so that the record is more ex- 
tended than in Figure 17. The echoes shown are of 
pings of various lengths from 0.4 yd to 80 yd, and 
all are for beam aspect. Each oscillogram shows three 
echoes received within a period of 10 sec, and it will 
be noted that these echoes have a structure similar 
to that discussed in Chapter 3 and illustrated in 
Figure 52 in connection with signals, which shows 
the effect of interference between the components 
of the resultant echo. Both “spool”- and “trans- 



Figure 19. Chemical recorder trace made while echo- 
ranging vessel circled a submarine, showing the varia- 
tion in echo length at different aspects. It is seen that 
at beam aspects the echo is of a length comparable 
with that of the signal. 


former ”-type envelopes can be distinguished. There 
is some reason for concluding that the two main 
* ‘blobs” noticeable in the shorter ping lengths are 
due to echoes from the hull and conning tower, 
respectively. The “tail” that is observable in each 
case is attributed to sound reflected from the sub- 
marine to the surface, back to the boat, and thence 
to the sonar. 


It is not possible to separate the component echoes 
by ear, or on the range recorder. On the latter, how- 
ever, it is possible to see the elongation that results 
from the extension of the target in the line of sight. 
This effect is discernible in the oscillograms of Fig- 
ure 17, but much more clearly evident in the range 
recorder trace illustrated in Figure 19. This trace was 
made while the echo ranging vessel circled a sub- 
marine. When the latter presents a beam aspect, the 
echo is short, being about equal in length to that of 
the outgoing signal; the latter is visible at the left 
edge of the trace. As the aspect changes, the differ- 
ence in range to the various secondary sources in- 
creases, with an accompanying increase in the length 
of the echo. 

This increase is theoretically equal to the length 
of the target in the line of sight. This dimension is 
proportional to the cosine of the aspect angle; in 
Figure 20 it is plotted against the aspect angle, shown 
by the solid curve. The indentations shown at bow 
and stern aspects are due to the shadows cast by the 
hull. The experimental values are shown by the 
dotted curve, which is seen to parallel the theoretical 
curve quite well. The observed echo lengths are con- 
sistently longer than those calculated on the basis of 
the length of the submarine; since the wake of a 
moving vessel returns an echo, the length of the 
wake should be included in the calculation, but this 
is a rather indefinite quantity. 


8 4 3 Echo Intensity as a Function of 
Aspect and Ping Length 

The separation of the individual secondary sources 
on a complex target has an effect also on the intensity 
of the echo. Let the target areas of the several parts 
of the target be represented by s h s 2 , s 3 , . . . s n . The 
nth one will then return an echo of intensity pro- 
portional to s n . If the sources are close enough to- 
gether so that their echoes overlap, the intensities of 
all of them will add, so that the resultant intensity 
will be proportional to Si + s 2 + S 3 + • . .+«»». 

If the individual sources are spaced more widely 
than the ping length, the echoes will not overlap, and 
the result will be an echo intensity that is succes- 
sively proportional to s h then to s 2 , then to s 3 , and 
so on. It follows that, under these circumstances, 
the echo intensity will vary rapidly, but will be 
lower, on the average, than when there is over- 
lapping. 


168 


TARGET STRENGTH AND ECHO LEVEL 



Figure 20. Elongation of the echo from a submarine for various aspects. The solid curve is the theoretical length 
of the echo for a very short ping. The dotted curve connects observed values of the echo length after correction for 
the actual ping length. They are seen to parallel the theoretical curve fairly well. The indentations at bow and stern 
aspects are due to the shadow cast by the hull of the target. 



RESULTS OF EXPERIMENTS AT SEA 


169 


COS 0 

BOW 

BEAM STERN 

0 .2 • .4 .6 .8 1.0 




Figure 21. Target strength as a function of ping length 
and aspect. The difference in target strengths between 
80-yd and 24-yd signals (T^-Tu) and between 80-yd 
and 8-yd signals (T i0 — T s ) are plotted against the 
cosine of the aspect angle, 0. (From NY STR.) 

This effect is shown very clearly by Figure 17. It 
is seen that at bow and quarter aspect the amplitude 
of the echoes from the 26.5-yd pings are noticeably 
larger than those from the 4.0-yd pings. However, 
the simple theory presented here has not been com- 
pletely verified by experiment. Early measurements 
made at San Diego at 24 kc indicated that echoes 
of 4.0-yd signals averaged about 4 db lower than 
those from 26.5-yd signals; and that echoes at beam 
aspect showed less dependence on signal length than 
echoes from bow and quarter aspects. Later meas- 
urements, however, reported no very significant 
dependence of target strength on signal length, for 
signals of 8, 24, and 80 yd. These measurements are 
portrayed graphically in Figure 21, in which the 
differences in target strengths between 80-} r d and 
24-vd signals (T m — T 24 ) and between 80-yd and 8-yd 


signals (Tso—T 8 ) are plotted against the cosine of 
the aspect angle 6. The differences are very small, 
and in view of the large scatter, not much significance 
can be attached to them. 


8 4 4 Dependence of Target Strength 
on Frequency 

Theoretical considerations suggest that the target 
strength of a scatterer will depend on the frequency 
of the incident sound only when the principal part 
of the echo is due to scattering by irregularities, the 
dimensions of which are of the order of magnitude 
of the wavelength of the incident sound. 

The evidence of direct measurements is incon- 
clusive. On one occasion it was found that the values 
of the target strength for sound of 60 kc were as 
much as 14 db higher than those obtained when 24- 
kc sound was used; on another occasion the target 
strengths of the two frequencies were nearly equal. 
In these experiments the transmission loss was esti- 
mated from earlier measurements. In view of the 
small amount of data on transmission at 60 kc and 
the known variability at all frequencies, the esti- 
mated values of H are of doubtful accuracy. 

Experiments performed at sea with spherical 
targets at frequencies ranging from 10 to 40 kc also 
provide no decisive evidence of systematic variation 
of target strength with frequency; any variations 
that were observed were less than the uncertainty 
of the calibration of the sonar gear. This agrees with 
the results obtained at very short range, already 
discussed in 8.1. 

8 4 5 Dependence of Target Strength on 
Range and Speed of Target 

The target strength of a submarine might be 
expected to depend on the speed provided the motion 
resulted in a layer of turbulent water or of bubbles 
surrounding the submarine. There is no experimental 
evidence of such an effect, but most measurements 
have been made on creeping submarines, where 
the effect, if it exists, might be expected to be 
small. 

Concerning the effect on target strength of range, 
it is evident that if the target is at a range sufficiently 
large to act as a point source, its target strength is 
independent of the range, for under such circum- 
stances it will always be completely and uniformly 




170 


TARGET STRENGTH AND ECHO LEVEL 


insonified by the beam at all ranges. At close ranges, 
this might not be the case, and then the target 
strength would vary with range, depending on just 
how much and which part of the target was inson- 
ified. This can be seen from Figure 22. 




Figure 22. Diagram illustrating the effect of range on 
target strength at close range, the target will present 
a greater or smaller surface to the sound beam as the 
distance between it and the projector (P) increases or 
decreases; at long ranges it is completely immersed in 
the sound beam, and a change of range does not affect 
the surface area exposed to the ping. 


s s ECHOES FROM WAKES AND 
ARTIFICIAL TARGETS 

8.5.i Echoes from Wakes 

The discussion of the acoustic properties of wakes 
in Section 6.1 makes it clear that wakes are factors 
to be reckoned with in echo ranging, for two reasons. 

1. The wake may act as an acoustic screen, and as 
a result the echoes from real targets that are beyond 
the wake may be weakened. In Section 6.1.2 it was 
mentioned that the echo from a buoy was reduced 
by 13 db after the passage of a 40-ft motor launch 
between the buoy and the sonar, and that the echo 
did not return to its original level for some 2 minutes. 

2. The wake itself may produce echoes that are 
so similar, in both intensity and character, to the 
echo produced by real targets, as to be easily con- 
fused with them (see Figure 5 of Chapter 6). 

The latter effect has been used by submarines in 
evasive tactics; the presumption being that if the 
submarine made a sharp turn the resultant curved 
wake (“knuckle”) would leave the enemy sound 
operator an extended false target to echo range on 


and increase the submarine’s chances for favorable 
action. However, the value of this maneuver has not 
been established. On the other hand, the wake left 
by a target vessel might conceivably provide means 
by which the vessel could be tracked acoustically, 
especially since the acoustic properties of a wake are 
known to persist over periods of half an hour or more, 
long after the visible traces of the ship’s passage 
have disappeared. 

The concept of target strength as applied to wakes 
is fully discussed in Sections 6.2.5 and 6.2.6. 

8 . 5.2 Artificial Targets 

Mention was made in Section 8.1 of the echo 
repeater, an artificial target designed for training 
personnel. An artificial target that has proved to 
have a variety of uses is the triplane. 

The Triplane 

The most obvious substitute for a submarine as an 
echo-ranging practice target is a large sphere, but 
the difficulty encountered in handling it at sea pre- 
cludes its use. Theoretical investigation shows that 



Figure 23. Triplanes viewed from different aspects. 

a system of three mutually perpendicular square 
planes of length L has a target strength equivalent 
to that of a sphere of diameter d given by 
4.34 V 

( 17 ) 

A 


ECHOES FROM WAKES AND ARTIFICIAL TARGETS 


171 


330* 0* 30* 



Figure 24A. Echo levels from 8-in. triplane at close range. Frequency = 40 kc; distance to triplane = 11.5 ft; sound 
level at triplane =43.5 db. Three orientations are shown in Figures 24 A, B, and C. (A) — (0, 0, 1) Plane, Z = 0. 

where X is the wavelength of the sound. The target this value is for the favorable aspect. Thus a triplane 
strength is expected to vary with the orientation and with planes 1 yd square has a theoretical target 


172 


TARGET STRENGTH AND ECHO LEVEL 



strength with 24-kc sound equivalent to that of a 2 yd square have been extensively used to provide 
60-yd sphere, or about 23 db, which is roughly the strong echoes for training purposes. Such a triplane 
target strength at beam aspect of a submarine. A is illustrated in Figure 23. 

triplane of the given size is easy to handle. Triplanes Triplane targets must be very accurately con- 



ECHOES FROM WAKES AND ARTIFICIAL TARGETS 


173 


330* 0° 30* 



structed; unless the faces are perfectly perpendicular, the measurements of target strengths that were 

the echo will be distorted and probably weakened. mentioned above 4 were a large number of data on 

The target strength of a triplane depends on its triplanes. These triplanes were small, the planes 

orientation with respect to the sound beam. Among measuring 8 or 10 in. It was observed that the target 


174 


TARGET STRENGTH AND ECHO LEVEL 


strengths of these specimens varied as much as 10 db 
at a given frequency for different orientations; for 
example, the actual target strengths for 30-kc sound 
varied from — 6 db to — 16 db (see Table 3). The 
theoretical target strength, according to equations 
(17) and (3), is zero db. Thus, while the measured 
values of the target strengths of spheres is consist- 
ently higher than the theoretical values (see Table 1 ) , 
that of triplanes appears to be consistently lower. 


Table 3. Target strengths of 8-in. metal triplanes. 4 


Plane of orientation 

(frequency, kc) 

0, 0, 1, 

2 = 0 
(T, db) 

1 , 1 , 0, 
x+y = o 
(T, db) 

1, 1, 1, 
x+y+z =0 
(T, db) 

20 

-12.7 

-14.2 

* -20.2 

30 

- 5.7 

- 5.0 

-16.4 

40 

- 4.1 

- 4.0 

-15.1 

50 

- 1.5 

+ 0.9 

-10.1 

60 

+ 0.3 

+ 1.8 

- 8.2 

70 

+ 1.2 

+ 2.2 

- 7.3 

80 

+ 1.6 

+ 3.1 

- 7.9 

90 

+ 2.1 

+ 4.7 

- 4.9 


The departure of actual triplanes from geometric 
perfection undoubtedly contributes to this. The vari- 


ation in echo level of an 8-in. triplane is illustrated 
in Figure 24A, B, C, for three different orientations 
of the triplane, which was slowly rotated while being 
insonified. Measured values of target strengths for 
various orientations and frequencies are shown in 
Table 3. 

Bubble Targets 

The fact that wakes of submarines are sources of 
perceptible echoes suggested that artificial wakes 
might form a deceptive target that would confuse an 
echo-ranging vessel in the attack phase. Investiga- 
tion of the problem disclosed that by means of 
chemicals, bubble screens could be laid that were 
imitations of real submarine echoes, except for the 
doppler effect. Moreover, it was found that bubble 
targets could effectively mask or quench an echo 
from a submarine. The German variety of device for 
generating bubble targets became quite generally 
known under the name Pillenwerfer. The effective- 
ness of this device was not great, since an experienced 
sonarman had no difficulty in distinguishing the 
echo from the submarine and ignoring that from 
the bubbles. 


Chapter 9 

MAXIMUM ECHO RANGES WHEN BACKGROUND NOISE 

IS LIMITING 


RECEIVER SENSITIVITY AND 
BACKGROUND NOISE 


9.1.1 Reception in General 

W hen the signal has been emitted, the trans- 
ducer connections are changed so that it can 
act as a receiver of sound waves, or hydrophone. The 
oscillations of the hydrophone plate reproduce the 
sound incident on it, but the frequency of this sound 
is too great to be perceptible to the human ear. This 
makes some kind of portrayal device necessary. The 
mechanical pressure of the sound waves is converted 
into alternating currents by the magnetostrictive or 
piezoelectric effect, as described in Chapter 7 ; these 
currents are fed into an amplifier, and the amplified 
currents are utilized to render the incident sounds 
perceptible in various ways. The customary methods 
of portrayal are : 

1 . The amplified currents may be heterodyned to 
sonic frequencies, converted to airborne sound waves 
and made audible, by means of a loudspeaker or 
headphones. 

2. The amplified voltage may be rectified and 
applied to a cathode-ray oscilloscope. The spot of 
this indicator is usually made to move along a 
vertical y axis to indicate range. The rectified voltage 
may be applied so as to cause the spot to deviate 
from straight line motion (deflection in the direction 
of the x axis) . The echo is then recognized by a greater 
z-axis deflection than that produced by rever- 
beration. 

3. In a second method of portrayal involving the 
use of a cathode-ray oscilloscope, the spot always 
moves in a straight line to indicate range. Its bright- 
ness is controlled by the rectified voltage from the 
receiver, so that the echo appears as a bright spot on 
the relatively dim, or invisible, line traced by the 
spot in the absence of an. echo. This is called z-axis 
portrayal. It is possible to combine z- and z-axis 
portrayal. 

4. By using a chemical effect of the current, the 
sounds can be recorded on specially treated paper, 
the blackness of the trace being determined again 


by the magnitude of the current. This is thus similar 
to a z-axis portrayal. An advantage of this method, 
not possessed by the other two, is that it provides a 
comparatively permanent record of the incident 
sounds. The current is fed to the paper by a moving 
stylus, so that the range of an echo is also recorded. 

Although the three methods of portrayal are quite 
different, the general principles that govern them 
are similar. The echo is only one of many sounds 
picked up by the sonar. Each sound, whether wanted 
or unwanted, actuates the portrayal device. The 
echo must be heard in spite of the unwanted sounds 
that are being heard at the same time, or must be 
seen among the records of these other sounds. 

An ideal sonar would respond only to the echo 
and not to any other sound. This ideal is unattain- 
able, but some steps can be taken to approach it. For 
example, in listening to the radio we wish to hear 
the broadcast of only one station at a time, so we 
tune our set, with the result that it will respond only 
to the electric waves of the relatively narrow range 
of frequencies emitted by the particular station, and 
not to those of any other. In the same way, since 
the echo has a definite frequency, it will obviously 
be desirable to tune the receiver to this frequency, 
thus excluding much of the unwanted sound. This is 
more important with visual than with aural methods 
of portrayal, for the ear has the ability to ignore un- 
wanted sounds and to hear a note of definite pitch 
even in the presence of noise (see below and also 
Chapter 14). 

The tuning of the sonar receiver can be accom- 
plished at various stages. The first is the so-called 
radio-frequency (r-f) stage : the receiver can be tuned 
to the frequency of the incoming echo. In the second 
stage, the receiver is tuned to the intermediate 
frequency (i-f), which is the first heterodyne stage. 
Finally it is possible also to tune the receiver in the 
audio-frequency (a-f) stage, when the once-heter- 
odyned signal is heterodyned a second time to an 
audible frequency. The tuning is under the control 
of the operator, and can be accomplished at any one 
stage, or in several of them at once. 

Another line of approach is found in the fact that 
the echo is sound coming from a particular direction, 


175 


176 


MAXIMUM ECHO RANGES WHEN BACKGROUND NOISE IS LIMITING 


while background noises may come from all possible 
directions. The unwanted noise can be reduced by 
using directional hydrophones, as discussed in Sec- 
tion 7.4.3. The obvious disadvantage of such a 
receiver is that it cannot then be alert in all direc- 
tions simultaneously (although means have been 
found for circumventing this difficulty, as described 
in Chapter 11); but this drawback is offset by the 
consideration that, if an echo is received on a direc- 
tional sonar, the bearing of its source is at once 
known. 


9.1.2 Response Curves of Hydrophones 
and Amplifiers 

The Response of Hydrophones 

The electromotive force generated by the hydro- 
phone is a function of the sound pressure on its 
diaphragm. This response of the hydrophone par- 
tially determines the response of any system into 
which it may be connected. Hydrophone sensitivity 
at the frequency / is defined as the electromotive 
force developed in the hydrophone when it is in a 
sound field of frequency / and rms pressure of 1 
dyne/cm 2 . If e is the emf generated by the hydro- 
phone when in a sound field of p dynes/cm 2 , the ratio 


defines the sensitivity of the hydrophone. It is 
measured in volts/dyne/cm 2 . The quantity 

e 2 

K = 10 log k 2 = 10 log — 

p 2 

= 20 log k, (2) 

is called the response of the hydrophone. The re- 
sponse is the decibel ratio of the power generated by 
the hydrophone per ohm resistance of the external 
circuit to the intensity of the sound field at the 
hydrophone. For if 

P = the power per ohm resistance, 

/ = the intensity of the sound, 

then, since P = e 2 , and according to equation (4) of 
Chapter 1, I = p 2 , 

e 2 

K— 10 log — 

p 2 

P 

= 10 log (3) 


Response Curves 

The graph showing the response at each frequency 
is called the response curve of the system. The re- 
sponse curves of two QC magnetostriction trans- 
ducers are shown in Figure 1. They respond well 
only to sounds in the neighborhood of the resonance 
frequency / 0 . In the case of the QCJ, Figure lA,/ 0 is 

f,KC 


15 20 25 30 




24 kc; the transducer is said to resonate at 24 kc. The 
width w of the resonance peak, shown in the figure, 
is usually defined as the frequency separation of the 
two points on the curve which are 6 db below the 
maximum. In the given curve, w is seen to be about 
1 kc. 

Another commonly specified quantity is the 
resonance parameter Q=f 0 /w. If Q is greater than 
10 or 20, the system is said to be highly resonant; if 
Q is less than 4 or 5, the system is nonresonant. The 
QCJ transducer has a Q of about 24. The QCL shown 
in Figure IB is seen to be more sharply resonant than 
the QCJ; its w is about 200 or 300 c, and, since it 



RECEIVER SENSITIVITY AND BACKGROUND NOISE 


177 


resonates at 21 kc, its Q is 60 or 100. Because of the 
resonant character of these transducers, they them- 
selves are tuned, i.e., the echo frequency must be 
near the resonant frequency, otherwise they will not 
respond effectively. 

Response of Amplifiers 

The amplification ratio of an amplifier is similar 
to the hydrophone sensitivity. It is the ratio of the 
output- to the input-voltage. The response is defined 
in terms of amplification ratio in exactly the same 
manner that the response of a hydrophone is defined 
in terms of its sensitivity. Response curves can be 
plotted for amplifiers as well as hydrophones, and 
the same terminology is applied to them. 

9.1.3 Spectrum Level and Response Time 

Power Spectrum Level of Noise 

The response curve shows the emf generated by a 
hydrophone in responding to a sound of a definite 
frequency. Most of the unwanted sounds encoun- 
tered in echo ranging do not have a definite fre- 
quency, and it is necessary to consider the emf gener- 
ated by the hydrophone in response to such a sound. 

Consider an ideal hydrophone whose response 
curve is rectangular, as illustrated in Figure 2. Sup- 


frequency 



Figure 2. Schematic response curve of ideal hydro- 
phone. 


pose that it is possible in some way to vary both / 0 
and w, while the hydrophone is exposed to a constant 
noise. The emf generated will then depend on both 
/o and w. If w is made successively smaller and 
smaller, it will be found that the power P of the 
generated emf finally becomes proportional to w: 

P = WI(fo)w. (4) 


The two other factors in this equation are k, the 
sensitivity of the hydrophone to a sound of the fre- 
quency / 0 , as defined by equation (1), and a function 
/(/o) which is found to be characteristic of a partic- 
ular noise. This function has not been given a 
simple name, but is sometimes called the intensity 
of the noise in a 1-c band. The function 

N(f 0 ) = 10 log Z(/o) (5) 

is called the spectrum of the noise, or its spectrum 
level at / 0 . In order to distinguish the spectrum of a 
continuous noise from that of a pulse, it is often 
necessary to call the former a power spectrum and 
the latter an energy spectrum. Equation (4) then 
becomes 

10 log P = K + N + 10 log w. (6) 

In Part III, it will be necessary to consider the 
generalization of equation (4) for hydrophones whose 
response curves are not rectangular and narrow. For 
all wide-band noises encountered in echo ranging, 
however, it will be sufficiently accurate to use 
equation (4) even for resonant hydrophones like the 
QC, whose response curves are far from ideal. The 
definitions of K and w given in Section 9.1.2 are to 
be used. Equation (4) indicates that the power gen- 
erated by a wide-band noise is proportional to the 
width of the resonance peak of the transducer. 

Energy Spectrum Level of a Pulse 

Although the intensity of an uninterrupted, con- 
stant sound is most conveniently measured in terms 
of power (energy/sec), the intensity of a pulse is 
better measured in terms of energy, i.e., power times 
duration. The energy spectrum of a pulse can be 
defined in much the same manner as the power 
spectrum of an uninterrupted sound was defined 
above. 

If the pulse consists of a train of sinusoidal waves, 
it will have a more or less definite pitch, say / c, 
provided the train contains many complete waves. 
The definite pitch of such a pulse indicates that its 
energy spectrum will have a sharp maximum at the 
frequency /. If the number of waves in the train is 
diminished, the height of this peak decreases, and 
its width w increases. The complete mathematical 
discussion of this effect can be given an elaborate 
form, but the essential result is simple. 

Let the duration of the wave train be r sec. Each 
wave requires 1/f sec to pass a given point; therefore, 


178 


MAXIMUM ECHO RANGES WHEN BACKGROUND NOISE IS LIMITING 


A 



( 2 ) 


li 

FREQUENCY, £ 


I- 

D 

Ol 

Z 


TIME 


SHORT 

PULSE 



NARROW FILTER 


Figure 3. Response time of a filter in relation to its bandwidth. (A) Curves (1) and (2) represent diagrammatically the 
input of a long and short pulse respectively; (B) Graph at left is a schematic response curve of a wide filter. Curves 
(1) and (2) show diagrammatically the output of such a filter for the long and short pulse shown in A. The time response 
for the filter is indicated as t r ; (C) similar to B for a narrow filter. 


if the wave train contains many complete waves, 
iOM//. The duration of the pulse r and the width 
of the resonance peak of the pulse w are connected 
by the approximate equation 

wt= 1 . (7) 

The greater width of the resonance peak associated 
with a shorter pulse duration makes it appear that a 
short pulse can be analyzed into a much wider group 
of frequencies than a long one. The human ear be- 
haves in a manner consistent with this mathematical 
fact. If a listener hears pulses consisting of trains of 
sinusoidal waves, his sensations will depend on the 
number of waves in the train. If the pulse contains 
many complete waves, the sensation will be that of 
a short tone of well-defined pitch. As the number of 
complete waves diminishes, and the pulse becomes 
shorter, the listener finds it more and more difficult 
to be sure of the pitch. Finally, very short pulses 
consisting only of two or three waves lose all tonal 
characteristics and are best described as “clicks” or 
“pops.” 


Response of Band Filters to Short Pings 

Since the width of the spectrum peak of a pulse is 
inversely proportional to the pulse duration, it might 
be expected that in designing filters intended to pass 
only a restricted group of frequencies centered at 
/ c, the duration of the pulse would have to be taken 
into account. For since a very short pulse has a wider 
peak, it seems obvious that if a filter is to pass it with 
a minimum diminution of intensity, the width of the 
filter will have to be greater than is necessary for a 
longer pulse with its proportionately narrower peak. 

This can be stated in another way. There is a 
relation between the width of the filter and the speed 
with which it will respond to sudden changes of in- 
put. This is illustrated in Figure 3. The two upper 
graphs, A(l) and A(2), represent the input of a long 
and a short pulse, respectively. The graph at the left 
in row B shows the frequency response curve of a 
wide filter; the one at the left in row C, that of a 
narrow filter. The remaining curves, B(l) and B(2), 
C(l) and C(2), represent the outputs of the filters 


RECEIVER SENSITIVITY AND BACKGROUND NOISE 


179 


when excited by the corresponding pulse shown in A. 

The input, in each case, begins and ends abruptly, 
as shown in A(l) and A(2). The output, however, in 
each case begins and ends gradually. It requires a 
certain time interval Ir to come anywhere near its 
maximum value. a This time interval is indicated in 
each of the diagrams, and it is seen that it is much 
shorter in the case of the wide filter B than of the 
narrow one C. The relation between the response 
time tR sec and the width w c of the filter is given 
by the inequality 

tR}-. ( 8 ) 

w 

In a well-designed filter, the equality may be as- 
sumed to hold ; but a poorly designed filter may have 
a response time considerably greater than l/w. 

The diagrams show that if the pulse is long enough, 
as illustrated by the curves marked (1), the response 
time is short enough so that the pulse can come near 
its maximum value even in the case of the narrow 
filter C(l). If the pulse is short, however, as illus- 
trated by the curves marked (2), it is seen that 
while the response time of the wide filter is short 
enough to permit the pulse to come up to maximum 
value B(2), this is not true for the narrow filter C(2) : 
before the response time has elapsed, the input 
ceases. Thus the output never attains its steady- 
state value, but is less than this. 

It follows that if a receiver is to respond fully to 
pings of a length r 0 yd, whose duration is thus 
2 r 0 /c = r 0 /800 sec, the pass band of the receiver must 
be at least so wide that w = 800/r 0 cycles per second. 

914 Limitations on the Use of 
Sharply Tuned Receivers 

There are a number of factors that prevent full 
exploitation of tuning as a method of eliminating the 
unwanted sounds besides the limitation on filter 
width set by the ping length. Several of these factors 
will be discussed briefly. 

Doppler Effect 

Even if the frequency of the emitted signal remains 
constant, the frequency of the echo will not always 

a Theoretically, it requires an infinite time to reach its 
maximum value, hence the rather vague wording of this 
sentence. 



Figure 4. Diagram showing how the range rate de- 
pends on the relative bearing of the target. 


be the same, but will depend on the rate at which 
the range of the target is changing. (See the discus- 
sion of the doppler effect in Section 10.2.) The tuning 
cannot be made indefinitely sharp, therefore, without 
endangering the reception of echoes from targets 
whose range rate is high. 

The change in frequency due to the doppler effect 
can be very considerable. In Chapter 10 it is shown 
that if the emitted frequency in kilocycles is / and 
the range rate of the target in knots is v, the fre- 
quency of the echo is changed by A / c, where 

Af = 0.7vf c. (9) 

The change Af is an increase if the range is closing 
and a decrease if it is opening. If the sonar vessel 
has a speed of 20 knots and the possible targets have 
speeds up to 4 knots, the possible echoes may have 
any frequency within a range of nearly 900 c. The 
pass band of the receiver must therefore be at least 
as wide as that. 

It is appropriate to note here that the range rate 
depends not only on the speeds of sonar vessel and 
target, but also on the relative bearing of the target. 
This is illustrated in Figure 4, which shows three 
successive positions of two vessels passing on con- 
stant courses at constant speeds. At time 1, the 
target is off the bow of the sonar vessel, and the 
range is closing rapidly. At time 2, the target is 
abeam, and the range rate is zero. At time 3, the 
target is on the quarter, and the range is opening 
rapidly. The change from closing to opening range 
occurs continuously as the bearing changes. 

Reverberation 

Reverberation occupies a peculiar position, as it 
is in some ways an unwanted sound and in others a 


180 


MAXIMUM ECHO RANGES WHEN BACKGROUND NOISE IS LIMITING 


wanted sound. It can mask the echo and is therefore 
an unwanted sound. From this point of view, it is 
unfortunate that its frequency is very close to that 
of the echo, so that extremely sharp tuning is needed 
if the receiver is to respond to the echo and not to 
the reverberation. 

Reverberation consists essentially of a large number 
of echoes, hence its frequency will also be affected 
by doppler. Since the scatterers responsible for the 
echoes are presumably at rest in the water, the range 
rate, and therefore the magnitude of the doppler 
effect, will be determined solely by the speed of the 
sonar vessel and the relative bearing of the sound 
beam. For this reason the doppler effect of reverbera- 
tion is called own doppler. If an echo is received from 
a moving target, there will be a difference between 
its frequency and that of the reverberation; this 
difference is called target doppler. The magnitude of 
the target doppler is a measure of the speed and 
approximate bearing of the target, hence an impor- 
tant item. As it enables the determination of target 
doppler, reverberation is a wanted sound. 

It will be shown in Chapter 10 that, when the 
difference in frequency between echo and reverber- 
ation is large and the echo is detected by ear, the 
masking power of the latter is reduced. It then 
functions primarily as a wanted sound. On the other 
hand, when the speed of the target through the water 
is small or at right angles to the transducer heading, 
the unwanted masking effect of reverberation is 
dominant. This unwanted effect is always the domi- 
nant one with visual methods of portrayal, since the 
range recorder cannot distinguish between sounds 
of various frequencies. 

Own-Doppler Nullifier 

It was seen above that the major limitation on the 
use of narrow band receivers is the necessity of allow- 
ing echoes of many different frequencies to pass 
through the receiver. The limitation would not be 
so severe if the sonar vessel were at rest, or if its 
motion did not affect the frequency of the echo: for 
the speed of the most common targets is relatively 
small, and it would be possible to reduce the width 
of the receiver band if this were the only cause of 
doppler shifts. 

It would be possible to operate with a narrow band 
receiver if the operator could constantly change the 
frequency of the transmitted signal by an amount 
just sufficient to compensate for the own doppler. 


The reverberation frequency would then remain con- 
stant, and the only frequency shift to be accom- 
modated would be that of target doppler. Because 
of the necessity of sweeping the sound beam over a 
wide range of bearings, the own doppler changes 
rapidly, and it is not feasible for the operator to 
make this adjustment and still perform his other 
duties. 

A device has therefore been developed that auto- 
matically accomplishes this result to a high degree 
of approximation. This is known as the own-doppler 
nullifier . 4 If this device is set for some one frequency 
/, the heterodyne frequency is automatically adjusted 
to this value during the first fraction of a second 
after transmission; thereafter the adjustment re- 
mains constant. In this way, the frequency of the 
reverberation is kept quite constant, and considerably 
narrower filters can be used in the receiver. This 
device may be less useful if submarines capable of 
high underwater speeds become more common. 

9 . 1.5 Discrimination of the Hydrophone 
against Noise 

Thus far it has been tacitly assumed that the 
hydrophone is nondirectional, or else that the noise 
source is located on the acoustic axis of the hydro- 
phone. In general, the sources of background noise 
are located at random, and it may be assumed that 
the noise is isotropic. This means that the sound 
energy incident on the hydrophone from any one 
direction is the same as that from any other direction. 

If the hydrophone is directional, it will then be 
relatively insensitive to sounds from most directions, 
and the emf generated will be only a fraction of that 
given by equation (4) . This fraction, when converted 
into db, is the directivity index D of the hydrophone 
(see Section 7.4). It is a negative number, since the 
fraction is less than unity. Equation (6) becomes 

10 log e = K-\- N-\-D -\- 10 log w (10) 
foradirectional hydrophone and nondirectional noise. 

9.1.0 The Inherent Threshold of 
a Hydrophone 

Any system capable of acting as a hydrophone, 
i.e., of generating an emf when a mechanical pressure 
is applied to it, will spontaneously generate an elec- 


RECEIVER SENSITIVITY AND BACKGROUND NOISE 


181 


tromotive force [emf ] even when no sound is incident 
on it. This is a consequence of the kinetic theory of 
heat. According to this theory, all the molecules of 
matter are constantly in motion. The energy of this 
motion is measured by the temperature. The higher 
the temperature, the greater the spontaneous in- 
ternal motion. 

The effect of the spontaneous motion is in many 
ways similar to that of the forced motion caused by 
a sound pressure. In particular, it causes an emf. 
When the hydrophone is connected through an am- 
plifier to a loudspeaker, this emf is heard as a hiss or 
crackle. It is in all respects similar to the sound of a 
wide-band noise received with the same hydrophone. 

Heat motion is not the only cause of spontaneous 
emf: joints on which soldering acid has been used 
are another source; loose connections of all kinds 
contribute. 

Let e 0 be the magnitude of the spontaneously 
generated emf of a hydrophone, whatever its cause. 
Since the sound produced by it when connected to a 
loudspeaker is similar to that of a wide-band noise, 
it is natural to calculate the spectrum level of the 
isotropic noise equivalent to the spontaneous emf. 
Referring to equations (6) and (10), this is 

iVo = 10 log — — if — £>. (11) 

w 

The quantity N 0 is called the inherent threshold of 
the hydrophone. A noise whose spectrum level is much 
less than No will not be audible above the sponta- 
neously generated noise. The inherent threshold of 
the hydrophone thus sets a lower limit to the level 
of the sounds that can be detected by it. 

9.1.7 Two General Specifications for 
the Echo-Ranging Receiver 

Everything that has been said concerning hydro- 
phones can be extended almost verbatim to the 
complex system composed of a hydrophone connected 
to a heterodyne amplifier. The emf generated in the 
output stages of the amplifier when a sound is in- 
cident on the hydrophone can be plotted as a re- 
sponse curve for the system as a whole. Adjustment 
of the amplifier gain will shift the response curve 
parallel to itself; adjustment of the tuning in any 
stage of the receiver will alter the value of the 
resonance frequency or the width of the resonance 
curve, or possibly both. 


The following discussion will be couched in terms 
of the loudspeaker presentation but can be applied 
with slight modification to any of the other methods 
of portrayal. If the transducer is trained on the 
bearing of a target and E is the sound level of the 
echo in the water, the sound emitted by the loud- 
speaker will have the level E &il where 

E air = E + A (12) 

and A is the gain of the receiver system. If there is 
an isotropic noise of spectrum level N incident on 
the transducer, the spectrum level of the sound 
emitted by the loudspeaker will be A a i r , where 

N &iT = N + D + A. (13) 

The entire receiver will also have an inherent 
threshold, the spontaneous emf being generated 
partly in the hydrophone, partly in the other portions 
of the circuits. Some additional increase of the in- 
herent threshold may result if these circuits are not 
adequately shielded from other electrical equipment 
aboard ship. 

The inherent noise of the whole receiver can be 
specified in two ways. Perhaps the most natural is 
to specify the spectrum level of the noise which issues 
from the loudspeaker when no underwater sound is 
incident on the transducer; this will be called N 0 , a ir. 
If this has been measured, one can calculate the 
underwater noise that is equivalent to it, No, by 
inverting equation (13) 

No = N o t& i T — D — A. (14) 

The operator will have to hear the echo in spite 
of the fact that he also hears the noise A a i r that has 
been picked up by the receiver from the water, and 
the noise N 0 , a ir that has been generated by the re- 
ceiver. In addition to this, he will also be disturbed 
by other extraneous sound resulting from activities 
aboard ship — suppose that their spectrum level is 

N ship. 

In order to obtain some idea of the proper design 
for the sonar receiver, three cases will be considered 
in turn. Suppose first that the shipboard sounds are 
more disturbing than the other two noises: A 8 hi P > 
N o.air and A S hi p > N & ir . The operator may try to 
remedy this by increasing the gain A. According to 
equation (12), this will increase E air and thus in- 
crease the loudness of the echo. 

If the shipboard sounds are not too loud, this will 
be an effective remedy, but there is a limit to the 
useful increase in gain. According to equation (13), 
the level of the noise picked up from the water will 
be increased by the same amount as the echo. The 


182 


MAXIMUM ECHO RANGES WHEN BACKGROUND NOISE IS LIMITING 


inherent noise will probably also be increased. The 
optimum gain setting will be such that one or both 
of these last two noises, N & „ and No, air, are com- 
fortably audible above the shipboard noises. When 
this is the case, the shipboard noises do not affect 
the audibility of the echo. 

This results in a first general specification for the 
design and location of sonar receivers. 

Specification 1. The gain of the receiver amplifier 
and loudspeaker system and their location aboard 
ship should be such that water noise or inherent 
noise, or both, can always be heard despite the sound 
of nearby activities. 

Neither the inherent noise at a given gain setting 
nor the water noise are under the control of the sonar 
operator. However, the former can be reduced by 
proper design, installation, and maintenance of the 
electronic components of the receiver. The reduction 
of water noise is more difficult than the reduction 
of inherent noise. Good practice will therefore require 
that Wo, air < N a ir or, which is the same thing, that 
No <N. This results in a second general specification. 

Specification 2. The inherent noise of the receiver 
should be so low that it is possible to hear the water 
noise. 


If these two specifications are complied with, the 
audibility of the echo will be determined solely by 
the reverberation level and the spectrum level of the 
water noise. The effect of reverberation will be dis- 
cussed in the next section of this chapter. No discus- 
sion of the ways and means of complying with these 
two general specifications will be given in this book. 

While it is essential to use enough gain so that 
water noise is comfortably audible, additional gain 
will have an adverse effect. Not only will the ex- 
cessive level of the speaker output be a source of 
discomfort to the operator, but there is danger that 
a signal may raise the level to the point of overload- 
ing the amplifier, causing it to operate inefficiently 
and reduce the audibility of the signal. 

9 2 BACKGROUND NOISE IN 

ECHO RANGING 

9.2.1 General Classification 

The background sounds have many causes, a 
partial list of them being given in Table 1. From the 
foregoing discussion it appears that it is convenient 


TABLE 1. CLASSIFICATION OF AMPLIFIED SOUNDS IN ECHO RANGING. 

I Background Noise. Extraneous sounds of various kinds. 

A. Self noise produced at or on own ship. 

1. Caused by motion of ship and/ or gear relative to water, or by the slapping 
of waves against the ship when stationary. 

2. Caused by mechanical vibration incident to operations aboard own ship 
and picked up by hydrophone. 

3. Circuit noise, caused by thermal agitation of the electrons, by instability 
of electric circuits in the receiver, by operation of ship’s power system, etc. 

B. Ambient noise produced at a distance from own ship. 

1 . (a) Sea noise, principal cause unknown — heard even in deep water. 

(b) Rain, surf, whitecaps are occasional causes. 

2. Biological noise: certain fish, shrimp, etc., produce sounds that are audible 
in sonic and supersonic gear. 

3. Traffic noise, caused by ship traffic and, in or near harbors, by industrial 
operations. 

C. Target noise produced at the target. This is the wanted sound in listening 

but an unwanted background in echo ranging, and may prevent accurate 

determination of the range of the target. 

II Reverberation. A sound which is an intrinsic accompaniment to all echo- 

ranging operations, caused by scattering of the emitted sound by 

1. Irregularities of sea bottom. 

2. Irregularities of sea surface. 

3. Unknown scattering mechanisms widely distributed throughout the volume 
of the sea. 


BACKGROUND NOISE IN ECHO RANGING 


183 


to distinguish between airborne noise that does not 
issue from the loudspeaker, and the noise from the 
loudspeaker, which may be called “amplified” noise. 

The amplified noise is of two general kinds. One 
kind is extraneous to the operation of the echo- 
ranging gear, and is heard even when no pings are 
emitted. This is the background noise. A sound that 
is inherent in echo ranging is reverberation, which 
has very nearly the same frequency as the ping or 
echo. In discussing the limitation of range in echo 
ranging, it is convenient to differentiate between the 
case where the range is limited by background noise 
and the case where reverberation is the limiting 
factor. The latter case is treated in Chapter 10; the 
former in the present chapter. 

The general classification of noise is given in Table 
1. A detailed description of the background noise 
will be found in Chapter 13. Table 2 supplements 


Table 2. Typical spectrum levels of amplified noise at 
24 kc. 


Self-noise 

Decibels 


Circuit noise 

- 104 to - 

94 

Submarine self-noise 

- 72 to - 

46 

Surface vessel self-noise 

DD or DE, 10 to 20 kc 3 

— 65 to — 

35 

Ambient noise 

Sea noise 

-74 to - 

54 

Biological noise 

Snapping shrimp 

-39 


Croakers 

-20 


Traffic noise (includes sea noise) 

-55 to - 

50 

Target noise (source levels) 

Submarine, 6 kt periscope depth, 12 kt surf. 

8 


Battleship 

27 


Cruiser 

20 


Destroyer 

15 


Passenger 

13 


Corvette 

8 


Freighter 

3 



the brief outline of Table 1 by giving some levels of 
the noise. These are the power spectrum levels de- 
fined in Section 9.1.3. 

9 . 2.2 Ambient Noise 

A comprehensive discussion of ambient noise will 
be found in Section 13.4. In echo ranging, ambient 
noise is important if the echo-ranging vessel is com- 
paratively quiet; in this event echoes may, under 
favorable circumstances, be received from long 
ranges, limited only by the masking effect of the 
inherent noise of the sea. 


While the mechanism of sea noise is not known in 
detail, it is known that it increases with wind force 
and sea state, and that its spectrum level decreases 
about 5 db each time the frequency is doubled. (See 
Figure 7 of Chapter 13.) 

Biological noise is not very important in echo 
ranging. Most of it is intermittent, or localized in 
small areas. The only incessant source of this type 
of noise is the snapping shrimp; but these animals 
live only in shallow water (less than 30 fathoms). In 
such areas the echo will nearly always be masked by 
reverberation from the bottom; for it is precisely the 
rocky, uneven type of bottom affected by snapping 
shrimp that is the source of the strongest bottom 
reverberation. However, shrimp noise may be an- 
noying, especially in harbor echo-ranging installa- 
tions in latitudes less than 40°. 

An important contribution to ambient noise is 
made by other ships moving in the neighborhood of 
the echo-ranging vessel, for example, in convoys. In 
and near harbors the noise of industrial and com- 
mercial operations (dredging, riveting on the hulls of 
ships in docks, etc.) is added to that of passing ships. 
This background noise is often dominant in harbor 
installations. 

The noise produced by the target vessel itself can 
perhaps be considered as traffic noise. In listening, 
these sounds are the wanted ones; and even while 
engaged in echo ranging, the operator will, between 
pings, listen for what the British call “hydrophone 
effect,” and attempt to gain some information about 
the target from its sounds. But the target noise may 
prevent an accurate determination of range and must 
therefore be considered as part of the masking back- 
ground. 

9 . 2.3 Self-Noise 

In echo ranging from fast-moving vessels it is the 
noise produced at the vessel itself that is likely to 
limit the range. The chief causes of self-noise are 
cavitation at the screws or near the transducer and 
the impact of air bubbles, caused by the passage of 
the hull through the water, against the transducer. 
The lower limit of self-noise is the inherent noise of 
the receiving system which is usually included in this 
category, although its cause is quite different. 

The level of self-noise increases with the speed of 
the echo-ranging vessel, as much as 3 db per knot 
increase in speed above 15 knots in the case of de- 
stroyers. Below 15 knots self-noise is not likely to be 


184 


MAXIMUM ECHO RANGES WHEN BACKGROUND NOISE IS LIMITING 


the limiting background, provided adequate main- 
tenance has kept the inherent noise of the system 
from becoming too great. 

Self-noise decreases rapidly with frequency; at 24 
kc it drops, on the average, about 8 db per octave 
increase in frequency. This is an argument in favor 
of the use of the highest practicable frequency in 
echo ranging. 

Self-noise is not likely to be important in echo 
ranging from submarines. When the submarine echo- 
ranges, it depends generally on a single ping for the 
echo; since the self-noise of submarines proceeding at 
high speed is appreciable, it will be reduced if the 
motors are shut down when echo ranging. It has 
been observed that this may reduce the self-noise by 
as much as 20 db. 1 

That part of the self-noise caused by the motion of 
the sonar projectors through the water can be reduced 
by enclosing them in streamlined structures. A first 
step in this direction was the construction of pro- 
jectors having a spherical shape, even though their 
diaphragms were plane. This was probably dictated 
as much by a desire to reduce the force required to 
move the projector through the water, as by con- 
sideration of the self-noise. 

However, this construction did not eliminate that 
part of the noise caused by the motion of bubbly 
water past the projector, and it became the practice 
to enclose the spherical projector in a larger stream- 
lined dome. In one case, it was found that the pres- 
ence of the dome decreased the noise level by 23 db 
when the ship was moving at 25 knots. 1 The problems 
connected with the design and use of such domes 
were discussed briefly in Chapter 7. 

9.3 THE RECOGNITION OF THE ECHO 

9.3.i Definition of Recognition and 
Maximum Range 

A signal of any kind will be clearly identified as 
such against a background of noise if it produces a 
sufficiently great change in the sound. The change 
may be in loudness, or pitch, or quality, or any com- 
bination of these three characteristics. As this change 
becomes smaller, a point will be reached at which 
repeated signals may be heard sometimes and not 
heard other times. By convention, recognition occurs 
when 50 per cent of the signals are correctly identified. 


When applying this definition to echoes, it can be 
stated in another way. When the target is at very 
long range an occasional echo may be received that 
can definitely be identified as such. As the range is 
closed, more and more of the transmitted pings will 
return identifiable echoes; when half of them do so, 
we say that recognition occurs. The range at which 
this occurs is called the maximum range , a term that 
has no other significance than this. It does not mean, 
on the one hand, that echoes will not be received 
from ranges longer than the maximum; nor, on the 
other hand, that at shorter ranges every ping will 
necessarily return a detectable echo. 

The 50 per cent criterion is arbitrary. The range 
recorder may exhibit a pattern which definitely in- 
dicates that echoes are being received even if the 
fraction of perceptible ones is considerably less than 
50 per cent; conversely, it is possible to be well 
within the maximum range and still fail to get a 
detectable echo if only a few pings are sent out. 

This definition of recognition is therefore inade- 
quate if the echo-ranging vessel is restricted to 1 or 2 
pings, as is the practice on submarines. In this case 
it is necessary to have practical certainty of recogni- 
tion, that is, 80 or 90 per cent probability of recog- 
nition instead of 50 per cent. When any probability 
other than 50 per cent is required, the per cent 
recognition is specified. 

9.3.2 The Recognition Differential 

The intensity required for a given signal (a pure 
tone, say, of a certain frequency) to be recognized 
depends on the intensity and character of the back- 
ground noise. The ratio, in db, of the power of the 
signal at recognition to the power of the noise in the 
pass band of the receiver is called the “recognition 
differential” for the particular set of conditions 
existing during the measurement of the signal-to- 
noise ratio. If the recognition differential is denoted 
by M , then 

M = E— L db, (15) 

where E = sound level of the echo at 50 per cent 
recognition, 

L = N -\- 10 log w = sound level of the back- 
ground noise, (16) 

N = spectrum level of the noise, 
w = bandwidth of the receiver, c. 


THE RECOGNITION OF THE ECHO 


185 


The factors that determine the recognition differen- 
tial can be classified into three general categories. 

1. Physical properties of the signal, its frequency 
and duration, as well as the physical character of 
the background noise. 

2. The characteristics of the gear and of the por- 
trayal apparatus. The chief of these is the width of 
the frequency band to which the receiver will respond ; 
this also affects the physical characteristics of the 
signal and noise. Its effect is only partially included 
in the equation L = N + 10 log w. 

3. Psychoacoustic factors, such as the subjective 
acuity of the observer, his skill and training, etc. 
These are related to the bandwidth and to the 
method of portrayal. 

We shall discuss the recognition differential at 
present with the main emphasis on the effect of 
bandwidth and ping length, leaving the more de- 
tailed discussion of the psychoacoustic factors to 
Chapter 14. A few remarks concerning the method 
of portrayal are pertinent here. 


9.3.3 Method of Portrayal 

Listening to the echo enables the operator to 
exploit the difference in quality between the echo 
and the background. Provided the signal is not of 
excessively short duration, the echo will be a musical 
tone of definite pitch contrasting markedly with the 
more or less steady hissing or crackling background. 
If the background is reverberation, the echo from a 
moving target will differ from the background in 
pitch, because of the doppler effect. These advan- 
tages are lost in visual portrayal methods; in these 
the distinguishing characteristic of the echo is 
primarily its greater intensity (see Figure 19 of 
Chapter 8). 

The range recorder has one advantage, resulting 
from the permanence of its record, which enables 
the operator to compare any number of echoes with 
each other. This “memory” is very valuable in the 
identification of echoes that are so weak that they 
can be heard, or seen on the record, only a small 
fraction of the time. 


9.3.4 Recognition 

The problem of recognition has many aspects. By 
way of introduction, an oversimplified case will be 
discussed, to serve as a basis for the later account of 



1000 




NOISE LEVEL, L,DB 


Figure 5. Diagram illustrating the case of a constant 
recognition differential. (A) Graph of L=iV+10 log w , 
(w = const.), and E = L+M; (B) graph of L=A+10 
log w, (N = const.) and E=L+M; (C) graph of 
M = E —L (M = const.). 


the complications. It will first be assumed that the 
recognition differential is independent of both the 
bandwidth of the receiver and of the spectrum level 
of the noise. The three graphs of Figure 5 illustrate 
this oversimplified case of a constant recognition 
differential. An increase of either the spectrum level 
N or bandwidth w causes a corresponding increase 
in the noise level L, according to equation (16), 

L = N + 10 log w. 



186 


MAXIMUM ECHO RANGES WHEN BACKGROUND NOISE IS LIMITING 




Figure 6. Diagram illustrating recognition with visual 
methods of portrayal. (A) Graphs of iV=Z, + 10 log w 
(w= const.) and E = L-\-M ; (B) value of recognition 
differential corresponding to the sound levels in A. 

The actual echo level is, of course, independent of 
both N and w, as is determined by quite other 
factors. However, the level E which is necessary for 
50 per cent recognition will be 

E = L + M (for 50 per cent recognition). (16a) 

For convenience, this will be called the recognition 
level of the echo. If the actual level is less than the 
recognition level, the echo will usually be lost. If it 
is greater, the echo will usually be detected. 

This simple case of a constant recognition differen- 
tial is not realized in practice by any of the methods 
of portrayal. A pair of graphs for the visual methods 
of portrayal are shown in Figure 6. The upper graph 
shows that, as the spectrum level increases, the noise 
level also increases. (Both the noise and echo levels 
are here to be interpreted in terms of the voltage 
applied to the range recorder or oscillograph.) How- 
ever, the echo level necessary for recognition remains 
more or less constant until a certain critical value of 
the noise level is reached, whereupon it increases 
more rapidly than the noise level. The lower graph 


shows the values of the recognition differential that 
correspond to the sound levels of the upper graph. 

The diagram is divided into two regions, marked 
threshold limited and masking limited. The noise level 
separating the two is called the threshold level of the 
recorder or oscilloscope. When the noise level is less 
than the threshold, no trace of the noise is visible on 
the recorder paper or oscillograph. When the noise 
level exceeds the threshold, the noise produces a 
record. 

In the threshold-limited region, the recognition 
level of the echo remains more or less constant and 
is very nearly equal to the threshold level of the 
noise. That is, the condition for detection is that the 
echo voltage be great enough to make a mark on the 
paper, or to deflect the oscillograph appreciably. The 
slight drop as the noise level approaches the thresh- 
old level is caused by “sensitization.” The echo volt- 
age is actually assisted in making a record by the 
presence of the noise. This is a well-known effect in 
photography : films that have been exposed to a very 
weak light are more sensitive than those which have 
been kept completely dark until use. To pursue the 
analogy, if the films have been exposed to stronger 
light before use, they are fogged. The masking- 
limited region, where the noise obscures the echo, is 
analogous to photographs on fogged film. 

Obviously, it will be good practice to operate at 
the region of minimum recognition level, if that is 
possible. Adjustment of the gain will accomplish 
this objective, provided the equipment is well 
designed. 

Recognition of heterodyned echoes by ear obeys 
much the same laws as visual recognition. The con- 
cepts of threshold and masking limitation are ap- 
plicable almost without change. It is not known 
whether the ear also exhibits the sensitization phe- 
nomenon. These matters will be discussed in Chapter 
14. The principal difference between visual and aural 
detection lies in the effect of receiver bandwidth w. 
The recognition differential for visual detection is 
(presumably) independent of w, but when the ear is 
used under masking-limited conditions, the band- 
width is important in determining its value. How- 
ever, since the overall level of the masking noise is 
also dependent on bandwidth, the situation in regard 
to recognition level is almost the exact reverse. This is 
strongly dependent on w for visual detection, and 
almost independent of w for aural detection. 

It will be assumed, in what follows, that the echo 
is a tone of constant frequency arid rather long 



THE RECOGNITION OF THE ECHO 


187 


BAND WIDTH, W, CYCLES 


10 100 1000 



Figure 7. (A) Diagram illustrating recognition of an 
echo of constant frequency and rather long duration, 
when the noise level is great enough to cause masking 
limited conditions for all bandwidths; (B) changes in 
recognition differential corresponding to (A). 

duration, and that the spectrum level is high enough 
to cause masking-limited conditions to prevail for 
all bandwidths. Then the facts, are as illustrated in 
Figure 7. The upper graph shows that, for small 
bandwidths, the recognition level of the echo in- 
creases parallel with the increase of noise level. At a 
certain critical bandwidth, w f , the two curves cross, 
and the necessary echo level becomes almost inde- 
pendent of bandwidth. The lower graph shows the 
corresponding changes in the recognition differential 
M. It has a small positive value for bandwidths less 
than becomes zero at w f , and for larger widths, 
becomes negative. The large negative values are 
one of the major advantages of the audio presen- 
tation. 

The sensations of the operator when listening to 
echoes parallel these graphs rather closely. When 
the bandwidth is less than w f , echo and noise are 
heard as a single blended sound, and recognition is 


caused almost entirely by a noticeable increase in 
loudness when the echo comes in. When the band- 
width is greater than w f , echo and noise are heard as 
two distinct, though simultaneous sounds, and the 
operator feels that he is able to ignore the noise and 
concentrate on the echo. To a very considerable 
extent, this feeling is not an illusion. 

The theory of the critical bandwidth will be dis- 
cussed in Chapter 14. For the present purpose, it is 
sufficient to remark that its numerical value depends 
on the frequency, and increases below 300 c and 
above 1,000 c. This is one reason for the choice of 800 
c as the standard audio frequency in echo-ranging 
devices. 

935 The Effect of Ping Length 
on Recognition 

In the case of audio presentation, the duration of 
the echo becomes important because the ear needs a 
finite time — about 0.2 sec — to respond completely 
to a sound, and hence a signal of shorter duration 
than this will not sound so loud as an equally intense 
one of longer duration. Moreover, it is probable that 
recognition occurs when the peak values of a fluctu- 
ating echo intensity coincide with minimum values 
of the noise intensity, and this will be more likely 
to occur if the signal is long. 

Some experimental data on the effect of ping 
length on recognition are exhibited in Figures 8 and 
9. Figure 8 shows the variation of the recognition 
differential for pulses of 800-c sound when masked 
by noise. The pass band used in taking the measure- 
ments was 1,000 c wide. The recognition differential, 
however, is calculated in terms of the spectrum level 
of the noise. It is seen to decrease with the pulse 
duration up to about 0.2 or 0.3 sec. Further increase 
in the duration causes less change in the recognition 
differential. Figure 9 shows the results of experiments 
in which actual (recorded) echoes from a submarine 
were masked by wide-band thermal noise; echoes 
from other aspects might have given different results. 
A similar reduction in the recognition differential is 
seen, but the spread for the short ping length is 
more than 10 db. Two different pass bands centered 
at 800 c were used, and the values of M , as before, 
converted to the standard bandwidth of 1 c. The 
right-hand ordinate scale shows the values of M 
when the noise level is measured in a 40-c band — the 
critical bandwidth at 800 c. 




188 


MAXIMUM ECHO RANGES WHEN BACKGROUND NOISE IS LIMITING 


PULSE DURATION, MILLISECONDS 



ECHO DURATION, MILLISECONDS 
I 10 100 1000 10,000 



SO* 

? 

25 2 
20 3 ? 

y 

h 
15 2 
O 

10 o 

5 2 


Figure 8. Effect of pulse on recognition of 800-c 
pulses masked by noise. 


Figure 9. Effect of echo duration on recognition of 
echoes masked by noise. 


Multiple Pulses 

A difficulty encountered in the use of extremely 
short pings is that their echoes are easily overlooked 
because they so closely resemble the occasional 
“pops” of noise. It was thought that the use of two 
or more pings in close succession might eliminate 
the difficulty. An experimental study indicated that 
recognition was improved somewhat by the use of 
double pings. 2 

y . 3.6 Values of the Recognition 
Differential 

It is not feasible to measure the recognition differ- 
ential experimentally while actually echo ranging at 
sea. The experimenter, therefore, endeavors to simu- 
late, as closely as is possible in the laboratory, the 
condition encountered in practice. The ambient 
noise in the sea is replaced by artificially generated 
thermal noise; its bandwidth and level are at his 
control. With regard to the signal, two kinds are 
used. Actual echoes from submarines can be recorded, 
and then played back at various known, controlled 
levels, or pure tones of various frequencies, generated 
by oscillators, can be used. In the following, the term 
“signal” will be restricted to the latter kind. They 
differ from echoes in that they have a rectangular 
envelope, i.e., the level remains constant throughout 
the duration of the signal; echoes, on the contrary, 
have irregular envelopes, because their level fluc- 
tuates more or less widely throughout their duration. 
For this reason, if one listens to two echoes of the 
same average level against the same background 
noise, the recognition differential may be different. 
For this and other reasons, the recognition differen- 


tial for echoes is usually stated within a range of 
several decibels (see Table 3). For convenience, 
the recognition differentials for 800-c signals and 
echoes are tabulated in Table 3. 


Table 3. Recognition differential (RD) for 800-c signal 
and echo in noise background (1-kc band). 


Ping length 
(msec) 

RD of signal 
(db) 

RD of echo 
(db) 

1 

16 


9 


5 + 5 

10 

2 


36 


—6 ± 1 

70 

-5 


80 


—3 ± 1 

100 

-7 


140 

-9 


200 

-9 


300 


-10 ±1 

600 

-12 



Values of the recognition differential of echoes in 
a background of reverberation will be given in 
Chapter 10. 

937 Recognition Probability 

From the above discussion, it is clear that the 
recognition differential determines only the echo 
level necessary for a 50 — 50 probability of recogni- 
tion. The importance of other recognition probabil- 
ities has already been stressed and will now be 
considered in greater detail. 

Figure 10 presents data obtained in the laboratory 
by playing recorded echoes at a definite level L f and 
allowing listeners to hear them when masked by 
noise. The 50 — 50 level is L, and the abscissa of the 



MAXIMUM ECHO RANGES WHEN BACKGROUND NOISE IS LIMITING 


189 


U-L,DB 


-12 -8 -4 0 4 8 12 16 



Figure 10. Recognition probability. The 50 per cent 
recognition level is L. Listeners heard recorded echoes 
at a level L'. The abscissa of the graph shows the 
amount by which L' exceeded L", the ordinate is the 
recognition probability. 

graph shows the amount by which L' exceeded L ; the 
ordinate is the recognition probability. A recognition 
probability of 90 per cent means that 9 out of 10 
echoes are identified as such, the tenth one being 
inaudible. It is seen that 90 per cent recognition 
requires a level 4 or 5 db higher than does 50 per 
cent recognition. Conversely, if the level is 4 or 5 db 
lower than the 50 per cent level, only 10 per cent 
of the echoes are heard. 

This laboratory experiment does not reproduce 
conditions at sea in one very important respect. It 
has been remarked that the echoes are played back 
at a fixed and definite level. At sea, successive echoes 
have quite different levels. This is shown by Figure 
1 1 ; if the average level of the echoes is E, this graph 
shows that only about 35 per cent of the echoes have 

l'-e.db 



Figure 11. Graph showing the fraction of echoes that 
have levels L' greater than the average level E. 


levels L’ that are greater than E. About 10 per cent 
have levels V more than 4 db greater than E, and 
10 per cent have levels more than 10 db less than E. 

This raises the question: what is the recognition 
probability when E, the average echo level at sea, 
exceeds the 50 per cent laboratory value L by a 
certain amount? The data of Figures 10 and 11 can 
be combined to give Figure 12, which answers this 
question. It shows that when E = L, the large num- 
ber of echoes that are below average reduce the 
recognition probability from 50 to 35 per cent. The 
50 per cent value is not reached until E is about 2 db 


E -L, DB 

-12 -8 -4 0 4 8 12 16 



















































































Figure 12. Graph showing recognition probability 
when E, the average echo level at sea, exceeds the 50 
per cent laboratory value L by the amounts shown by 
the abscissas. 


greater than L, and the 90 per cent value requires E 
to be nearly 12 db greater than L. 

In view of the importance of the 90 per cent 
recognition probability for submarine operations, it 
would be desirable to be able to predict, in advance 
of transmission, whether the echo will be above or 
below average. The outlook for such a development 
is not favorable. 


9.4 MAXIMUM ECHO RANGES WHEN 
BACKGROUND NOISE IS LIMITING 


941 General Principles of 

Range Calculation 

From the discussion of the preceding sections it 
appears that an echo will be recognized 50 per cent 
of the time if its level E satisfies the relation 

E = N + D + M+ 10 log w. (17) 

where N is the equivalent water-noise spectrum level, 
D the directivity index of the transducer, and M the 
recognition differential. The quantity N + D + M + 
10 log w is the recognition level defined above. 

From equation (9) of Chapter 8 the echo level E is 
given by E = S + T-2H(r), (18) 

where S is the source level ol the projector, T the 
strength of the target, and H{r) the transmission 
loss to the target, presumed to be equal for both 
outgoing and reflected sound. Comparison of equa- 
tions (17) and (18) indicates that one may expect to 
detect more than 50 per cent of the echoes from the 
target if 

2/7 (r) < S + T-(A + 10 1ogw + D + M). (19) 

The right-hand member of equation (19) can, for 
convenience, be defined as the available signal output. 
The actual level of the echo must be greater than 






190 


MAXIMUM ECHO RANGES WHEN BACKGROUND NOISE IS LIMITING 


the recognition level ; the total transmission loss must 
be less than the available signal output. As the range 
to the target increases, the value of H(r) will in- 
crease. At some range r max it will become equal to 
the available signal output; for longer ranges, the 
echo will be heard less than half the time and will 
rapidly become inaudible all of the time. 

The maximum range r max is defined as the greatest 
range at which the available signal output is at least 
equal to the two-way transmission loss. Equation 
(2) shows that the maximum range will depend on a 
large number of terms. Each of these has already 
been discussed in detail, but it will be useful to sum- 
marize the salient facts about each term that enters 
into equation (19). 

The source level S is characteristic of the sonar 
projector and its power supply. It is also conditioned 
by the dome in which the projector is mounted. A 
typical value for standard Navy installations is 
110 db. 

The target strength T is characteristic of the sub- 
marine or target. An average value for a submarine 
is 15 db, but if the target is small or presents an 
unfavorable aspect, the value may be as low as 5 db. 
For an especially favorable aspect, a large submarine 
may have T = 25 db. 

The noise level N + 10 log w depends both on the 
noise sources near and on the ship, and on the band- 
width of the receiver. A typical value of the latter is 
1 kc (10 log w = + 30 db). The spectrum level N 
varies from - 60 db in a favorable case to — 30 db 
for a destroyer at 20 knots. A typical value is - 45 db. 

The directivity index D characterizes the direc- 
tionality of the receiver. Its value is adversely 
affected by the use of sound domes unless the latter 
are very carefully designed and installed (Section 
7.7). Neglecting this cause of variation, its values 
for standard Navy sonars range only over a few db, 
the average being — 23 db. 

The recognition differential M depends on the 
method of portrayal, the bandwidth of the receiver, 
and the acuity and training of the operator. The 
average value for a bandwidth of 1,000 c may be 
taken to be 0 db, but values of + 10 and - 10 db are 
not uncommon. The value of -f- 10 is perhaps very 
high for a trained operator, and should be considered 
to apply only to untrained personnel with little 
aptitude. 

The transmission loss H(r) depends on oceano- 
graphic conditions, the most important being the 
thermal conditions in the ocean, although wind, sea, 


and (in shallow water) the bottom character all 
influence its value. 

The gain of the receiver is conspicuous by its ab- 
sence from equation (19), although common sense 
might lead one to expect it to exert an influence on 
the maximum range. The reason for its absence is to 
be found in the two general specifications for sonar 
gear that were formulated in Section 9.1. If the 
operator makes full use of the gain provided under 
these specifications, a further increase in the gain 
will not affect the maximum range until the amplifier 
overloads. At that stage, the maximum range will 
be reduced by an increase in gain. 

When operated at proper gain, the available signal 
output is almost independent of the receiver band- 
width for aural presentation. This is because ( N 
+ 10 log w ) + M{w) is independent of w. For visual 
presentation, the term M is independent of w , and 
the term 10 log w is not canceled out (compare 
Figures 5 and 7). 

942 Values of the Available Signal 

The numerical values given above are summarized 
in Table 4. It should be noted that even the favorable 


Table 4. Available echo levels. 



Unfavorable 

case 

Average 

case 

Favorable 

case 


(db) 

(db) 

(db) 

s 

110 

110 

110 

T 

5 

15 

25 

N + 10 log w 

0 

-15 

-30 

D 

-23 

-23 

-23 

M (1-kc band) 

10 

0 

-10 

Available signal 

128 

163 

198 


and unfavorable cases do not represent extremes, 
and that the variation in the available signal may 
be even greater than is shown by the table. However, 
it is thought that the most common values of the 
available signal will be within + 10 db of the value 
160 db. 

943 Calculation of the Maximum Range 

The maximum range is to be calculated, according 
to equation (19), by equating the two-way transmis- 
sion loss to the available signal. If the transmission 


MAXIMUM ECHO RANGES WHEN BACKGROUND NOISE IS LIMITING 


191 


RANGE, YD 

100 200 500 1,000 2,000 5^000 20,000 



Figure 13. Graphical calculation of maximum echo 
ranges under various thermal conditions. The curves 
1 to 5 correspond to the anomaly curves of Figure 14, 
Chapter 3. 

loss were given by the inverse square law, the cal- 
culation could be made with a table of logarithms, 
from the equation 

40 log r = Available signal. (20) 

Using the available signals of Table 4, this equation 
results in the following values of the maximum 
range : 

Unfavorable case Average case Favorable case 
1,600 yd 10,000 yd 90,000 yd 

Except for the unfavorable case, these values are far 
in excess of the ranges actually observed. The reason 


is obvious; this calculation assumes that the trans- 
mission anomaly is zero, whereas it actually has 
very appreciable values. 

In order to obtain more reasonable values for 
probable ranges, the empirical values of the trans- 
mission loss must be used. The anomaly graphs of 
Figure 14, Chapter 3, have been used to calculate 
the transmission loss curves of Figure 13. If the 
curves are to be used simply to obtain values of the 
one-way transmission loss, the left-hand scale is to 
be used. The right-hand scale shows the two-way 
loss, which is to be equated to the available signal. 
The dotted lines show the unfavorable, average, 
and favorable values of the available signal, as 
tabulated above. The intersection of these lines 
with the graph appropriate to the different thermal 
conditions are shown on the graphs. The resulting 
estimates of the maximum range are shown in 
Table 5. 


Table 5. Estimates of maximum range. 


Thermal 

condition 

Unfavorable 

Average 

Favorable 

1 

350 

600 

1,200 

2 

500 

1,050 

2,000 

3 

650 

1,800 

2,800 

4 

100 

2,200 

5,500 

5 

1,200 

3,100 

6,500 



Chapter 10 

MAXIMUM ECHO RANGES WHEN REVERBERATION 

IS LIMITING 


10 1 REVERBERATION IN 

ECHO RANGING 

lo.i i General Remarks 

I n echo ranging, background noise, in general, 
limits only the longer ranges. At short, and pos- 
sibly medium ranges, the echo must be detected 
against a background of reverberation. As a masking 
background, reverberation differs from a noise in 
several waj^s. Reverberation is a background con- 
centrated around a definite frequency, whereas the 
spectrum of noise comprises a very wide range of 
frequencies. The level of reverberation depends on 
the power output of the projector and decreases very 
rapidly, with range being very high at short ranges 
and very low at long ranges. Noise, on the contrary, 
is independent of the projector output and is the 
same at all ranges. Echoes are usually tones of a 
definite pitch and thus are not likely to be confused 
with such noise, except when very short ping 
lengths are used. The occasional strong bursts of 
reverberation, however, may easily be mistaken for 
echoes. 

10 . 1.2 Spectrum of Reverberation 

The dependence of reverberation on power output 
and ping length were discussed in Chapter 5, where 
it was shown that the intensity of reverberation was 
proportional to these two factors. The spectrum of 
reverberation is of particular importance in discuss- 
ing the masking effect of reverberation. 

Figure 1 shows a typical spectrum of heterodyned 
reverberation from an 80-yd ping. The reverberation 
is seen to be concentrated around 840 c, the peak 
being only 24 c wide at the — 3-db points and 50 c 
wide at the — 10-db points. 

Theoretically, the power spectrum of reverberation 
should be the same as the energy spectrum of the 
ping which causes it. This conclusion depends on 
several assumptions, and it is not surprising that it 
is confirmed only in a general way. With long pings, 


the spectrum of reverberation has a well-defined 
peak, but its width is probably greater than that of 
the energy spectrum of the ping. As was noted above, 
this latter is 1 /r, where r is the duration of the ping 
in seconds. There are many possible reasons for 
this, but the effect has not been adequately studied. 
For sufficiently short pings, it may be that the 
spectrum of reverberation and ping become more 
nearly identical. In any case, it is safe to assume 
that the width of the spectrum peak for reverbera- 
tion is not less than 1/r. For pings of 0.1-sec 
duration such as are used in much echo-ranging 
work, Figure 1 shows that the width is about 24 c, 
rather than 10 c. 

FREQUENCY, CPS 


780 800 820 840 860 880 900 



The concentration of the reverberation about one 
frequency leads to a further important difference 
between reverberation and noise. This difference 
concerns the effect of the receiver bandwidth. If the 


192 


DOPPLER EFFECT 


193 


bandwidth is wide enough to admit frequencies about 
50 c to each side of the reverberation frequency, 
further increase in bandwidth will have no effect on 
the intensity of the reverberation emitted by the 
loudspeaker. Unlike noise, therefore, the airborne 
level of reverberation does not increase with band- 
width. Thus for a receiver having a response curve 
of the type shown in Figure 1 of Chapter 9 with a 
bandwidth of about 1 ,000 c or even less, the airborne 
reverberation level is simply 

R &ir = R + A, (1) 

just as for the echo equation (12) of Chapter 9. 

10 2 DOPPLER EFFECT 


10.2.1 Explanation of Doppler Effect 

When an observer is in motion toward a source of 
sound, he hears a note the pitch of which is higher 
than when he is at rest. If the observer is in motion 
away from the source, he hears a lower note than 
when he is at rest. Thus the apparent frequency of 
the sound is increased when an observer moves 
toward a source and decreased when he moves away 
from it. Similarly, if the source is moving toward 
the observer, the frequency is higher; if the source 
moves away from the observer, it is lower. This 
change in pitch is known as the doppler effect. 

The apparent frequency of the sound is found as 
follows. When the observer is at rest, the number of 
waves he receives each second is F 0 , the true fre- 
quency of the sound. When the observer is in motion 
toward the source, he receives more sound waves in 
each second than when he is at rest. If his mean 
range rate is v, the additional number of waves re- 
ceived per second are those which occupy this dis- 
tance, v, by which the range is changed in 1 sec. 
Since the distance between successive waves is the 
wavelength X, this number is v/\. Using the relation 
for the velocity c of the sound, 

c = F oX, 

the number of additional waves received is Fov/c. 
The apparent frequency F is the total number of 
waves received each second, and is therefore given by 

F = F 0 (l+- 



For the case in which the observer is in motion away 
from the source, the plus is replaced by a minus : 

If the source is receiving echoes from a target, the 
doppler effect will occur twice, so that the frequency 
of the echo Fe received at the source is 




Equation (4) gives the apparent frequency of the 
echo when the range rate is v, the positive sign being 
used if they are moving toward each other, the 
negative if they are moving away. 

The equations apply to the supersonic frequency 
of the sound in the water. In order to make this 
sound audible, the received waves ‘are heterodyned 
in the receiver. This heterodyne receiver reduces the 
frequency by a constant amount. It is important to 
note that this reduction is subtractive and not 
proportional, i.e., the receiver subtracts a constant 
amount Fh from the received frequency F, so that 
the audio frequency of the output is 

f=F — F h . (5) 

Applying this to equation (4), it is seen that the 
audio frequency of the echo is 


h: — Fq — F h + 

2 F 0 v 
= /o ± . 


2 FqV 
c 


(6) 

( 7 ) 


Here fo = F 0 —F H is the audio frequency of the echo 
for a zero range rate. The difference fs —fo, i.e., the 
quantity ± 2 F Q v/c, is called the absolute doppler shift. 
It is seen to be proportional to F 0 , and independent 
of Fn or / 0 . Since the transmitted frequency F 0 is 
much greater than the heterodyned audio frequency 
fo, this is a very important point. Using c = 2,800 
khots, and expressing v in knots, F 0 in kc, the doppler 
shift is 

fE—fo = 0.7 F 0 v c, approximately. (8) 
If Fo = 24 kc, 

fs— fo= 17 v c, approximately. (9) 

This shift can be very appreciable. If the sonar 
ship and target are on opposite courses, the one mov- 
ing at 24 knots, the other at 5, the shift is 30 X 17 = 
510 c. Since / 0 is commonly 800 c, this is a very large 


194 


MAXIMUM ECHO RANGES WHEN REVERBERATION IS LIMITING 


effect. Its importance in determining the width of 
the pass band of sonar receivers has already been 
discussed in Chapter 9. Other consequences will now 
be considered. 


10 . 2.2 Application to Echo Ranging 


In echo ranging the operator does not hear the 
outgoing ping, since the equipment is on “send” and 
the receiver is blocked. It is therefore impossible for 
him to compare the frequency of the returning echo 
with that of the outgoing ping. He can, however, 
compare the frequency of the echo with that of the 
reverberation heard immediately after the ping is 
emitted, and this has an important effect. The dif- 
ference between the reverberation and echo fre- 
quency depends only on the submarine’s absolute 
motion through the water, and its direction relative 
to the sound beam. It is independent of the motion 
of the ship. 

The reason for this may be explained as follows. 
Suppose the ship is moving with velocity V, its sound 
beam being directed dead ahead; then, just as in the 
case of an echo, the relative motion between the 
source and the scatterers will cause the reverberation 
frequency to increase, its value after heterodyning 
being given by equation (7) : 

2 F 0 V 

}r =/o H . (10) 

c 


If a submarine is approaching the echo-ranging 
ship with a speed V', the relative speed v is 

v = v+r, (id 


and the audio frequency of the echo is, from equa- 
tion (7), 


2 F 0 V 2 F 0 V' 

Se =/oH \ ■ 

c c 


( 12 ) 


Comparing equations (10) and (12), it is seen that 
the audio frequency of the echo exceeds that of the 
reverberation by 


Af = 


2 F 0 V' 
c 


(13) 


an expression that does not contain V, the speed of 
the sonar vessel. 

If Fo = 24 kc, 

A/ = 17 V' c, approximately; (14) 

thus, for an approaching 5-knot submarine, the fre- 


quency of the echo is 85 c above the reverberation 
frequency. As has already been mentioned, the 
quantity A / is known as the target doppler; because 
operationally it is much more important than the 
absolute doppler shift, it is frequently called simply 
doppler. It is “up-doppler” if the submarine is mov- 
ing toward the echo-ranging ship and “down-dop- 
pler” if it is moving away. 

In the above example, it has been assumed that 
the course of the target is directly toward (or away 
from) the echo-ranging gear. It may be shown that, 
in general, V' is not the actual speed of the target, 
but its range rate relative to a stationary point P. 
This point P momentarily coincides with the sonar 
projector, but must be considered stationary even 
though the sonar is moving. 


10.2.3 Importance of Target Doppler 

The importance of target doppler in echo ranging 
is immediately evident. It is a common experience 
that a difference in pitch between two tones is a 
great aid in hearing them, and even a very weak 
tone can often be distinguished from others if its 
pitch differs markedly. Thus target doppler is a great 
aid in detecting echoes against a reverberation back- 
ground. (It does not enter, of course, when the echo 
must be recognized against noise.) This application 
of target doppler to echo ranging will be discussed 
in the next section. 

A second important exploitation of target doppler 
derives from the fact that it is proportional to the 
speed of the target. Hence it can give information 
concerning the motion of the latter. If the echo is of 
higher frequency than the reverberation (up-doppler) , 
the range must be closing; if the echo frequency is 
lower than that of the reverberation, the range is 
opening. A trained operator can also estimate the 
probable aspect of the target with considerable ac- 
curacy from the change in target doppler. 

The ability of the operator to estimate the differ- 
ence in frequency between reverberation and echo 
depends on the ping length. This has been mentioned 
in Section 9.1. It is shown quantitatively by Figure 
3 of Chapter 14. 

Many “false” echoes are received from floating 
debris, kelp, and from unknown causes. These do 
not show the effect of target doppler, so that a final 
important application of the latter is this identifica- 
tion problem. 


RECOGNITION OF THE ECHO AGAINST REVERBERATION 


195 


10 3 RECOGNITION OF THE ECHO 
AGAINST REVERBERATION 

The definition of recognition and maximum range 
are the same for reverberation as for noise (Section 
9.3.1). Thus recognition occurs when 50 per cent of 
the echoes are correctly identified against the re- 
verberation; the range at which this would occur is 
the maximum reverberation limited range. This may 
be the actual maximum range, or not, as will be 
explained in Section 10.4.2. 

10.3.1 The Recognition Differential 

The recognition differential for reverberation is 
defined by 

M r = 10 log (15) 

Ir 

where I s = echo intensity at 50 per cent recognition, 
Ir = reverberation intensity. 

Using equation (9a) of Chapter 5 
E = 10 log /», 

and defining the absolute reverberation level R by 
R = 10 log Ir, (16) 

equation (15) can be written 

E = R + M r (17) 

and is exactly analogous to equation (16a) of 
Chapter 9 : 

E = L -f- Mn. 

The subscripts N and R will be used with M to 
distinguish between the two recognition differentials. 
In either case M is seen to be the number of decibels 
by which the echo must exceed the background 
(noise L or reverberation R), in order to be detected 
50 per cent of the time. The quantities R — Mr and 
L — Mn will be called the recognition level for rever- 
beration and recognition level for noise, respectively. 

In general, the factors that determine the recog- 
nition differential for reverberation are the same as 
those discussed in Section 9.3.2 in connection with 
noise. Very little work, however, has been done to 
investigate any but aural recognition. This is pri- 
marily due to the almost universal use of the ear 
for detection, even when other methods are used in 
addition. The discussion in the remaining sections of 
this chapter will therefore be restricted to aural detec- 
tion. The method of calculating maximum ranges, 


however, is applicable to all methods of presentation, 
provided, of course, the values of Mr which are 
used are appropriate to the particular presentation 
employed. 

10 3.2 Aural Recognition 

In Section 9.3.4 it was pointed out that in the case 
of the ear, the masking effect of background noise 
is restricted to a certain critical band of frequencies. 
In listening to an echo, the only part of the back- 
ground which is effective in masking is that part 
which is contained in the critical band centered at 
the echo frequency. For a heterodyned output of 800 
c, the critical band of the ear is about 40 c. 

For this reason it is clear from Figure 1 that if the 
echo has no doppler, i.e., its frequency is the same 
as that of the reverberation, virtually all of the 
reverberation power will be included in the critical 
band, and the ear has no advantage over other 
methods of presentation. On the other hand, when 
doppler shifts the echo 40 c or more away from the 
reverberation frequency, the level of reverberation 
in the critical band will be relatively low. Its masking 
effect will be correspondingly lower, with the result 
that weaker echoes can be detected. 

The effect of doppler shift on recognition can also 
be described in terms of the sensations of the op- 
erator. When the echo and reverberation have the 
same frequency, he will hear the echo only as a 
louder pulse of sound. As the frequency difference 
increases, he will become increasingly aware of a 
difference in pitch, until finally this will be the 
primary sensation. The difference in loudness will 
not be noticed unless it is extreme. 

10 . 3.3 Values of the Aural Recognition 
Differential 

The value of Mr for aural presentation depends 
on the duration of the echo and upon its doppler 
shift. Figure 2 shows the dependence of Mr on ping- 
duration for a beam echo having no doppler. For 
long signals (more than 200 msec) the recognition 
differential is nearly zero, indicating that the echo 
can be heard half the time if its level is equal to that 
of the reverberation. For signals shorter than 30 msec 
the echo level must exceed the reverberation by 
about 12 db in order for 50 per cent recognition to 


196 


MAXIMUM ECHO RANGES WHEN REVERBERATION IS LIMITING 


PING DURATION, MS 



Figure 2. Dependence of the recognition differential 
on ping duration for a beam echo without doppler, 
when masked by reverberation. 


occur. Between 30 and 200 msec Mr decreases 
approximately inversely as the ping duration. 

Now suppose the echo has doppler; as the mag- 
nitude of the doppler shift increases, the recognition 
differential decreases. This is shown in Figure 3 for 



Figure 3. Graph showing the reduction in recognition 
differential for dopplered echoes. Echo duration = 114 
msec. Note the asymmetry of the curve. 

1 14-msec echoes. The data were obtained by UCD WR 
using relatively well-trained subjects, representative 
of the best sonar operators. It is seen that the recog- 
nition differential is reduced 10 db by a target dop- 


pler of about — 25 c or -f 30 c; and 20 db by a target 
doppler of — 70 c or + 90 c. The asymmetry of the 
curve is interesting, as appearing to indicate that 
recognition is somewhat easier when the range is 
closing than when it is opening. Data obtained by 
other experimenters show this same asymmetry, but 
differ in some respects from Figure 3. 

This curve shows the great importance of target 
doppler in the recognition of echoes. From Figure 2 
it is seen that the recognition differential for a 114- 
msec echo is 6 db without doppler; if the range rate 
is 1.5 knots, the recognition differential is —4 db, 
and for a range rate of 5 knots, the recognition 
differential is about — 14 db. 

For ping lengths shorter than 114 msec the pitch 
discrimination of the ear is less, and the decrease in 
Mr will not be so great. For longer pings the discrim- 
ination improves and the decrease in Mr will be 
somewhat greater. Relatively little quantitative in- 
formation is available. 


10 4 MAXIMUM ECHO RANGES WHEN 
REVERBERATION IS LIMITING 


10 4 i General Principles of 

Range Calculations 

The calculation of reverberation-limited ranges 
differs from the calculation of noise-limited ranges 
only in one important feature: reverberation is a 
function of range, whereas noise is essentially con- 
stant. When reverberation is limiting, therefore, 
both the echo level and the background depend on 
range, and a slightly different method must be used 
to calculate the limiting range. 

By definition, the maximum range is the range for 
which equation (17) is satisfied, 

E = R + Mr. (17) 

To find the maximum range we may first plot a curve 
of E as a function of range, and next, a curve of 
R-\- Mr) the point at which the two curves intersect 
gives the maximum reverberation-limited range. 

Curves of E and R-\-Mr for a shallow target are 
shown in Figure 4 and will be discussed quantitatively 
in the next section. The recognition level for noise 
L + M n is also shown. The five echo-level curves cor- 
respond to the five thermal conditions used in Figure 

11 of Chapter 9 in the discussion of noise-limited 


MAXIMUM ECHO RANGES WHEN REVERBERATION IS LIMITING 


197 


RANGE, Y6 



Figure 4. Graphical estimation of maximum echo 
ranges limited by either reverberation or noise, for the 5 
thermal conditions shown in Figure 14 of Chapter 3 
and used to construct Figure 11 of Chapter 9. Curves 
1 to 5 show the echo level calculated for these thermal 
conditions. The curve marked R + Mr shows the 
recognition level with a reverberation background, and 
the broken curve marked L+Mn gives the recognition 
level when the masking background is noise. 

ranges. At very short ranges the echo level is seen 
to be far above both reverberation and noise, so that 
an echo at these ranges would rarely be masked. At 
longer ranges the echo level drops into either noise 
or reverberation. Thus the echo-level curves 1, 2, 
and 3 drop into reverberation before they reach the 
noise background. For these curves, therefore, re- 
verberation is the masking background. Curve 4, on 
the other hand, drops into noise before it reaches 
the reverberation, and noise is the masking back- 
ground. Curve 5 is also masked by noise; it does not 
intersect the reverberation curve at any range. 

The manner in which the various parameters enter 
into the range calculation may be shown as follows: 

1. The echo level is given by equation (9) of 
Chapter 8, 

E(r) = S+T-2H(r). 

2. Using equation (16) and equation (25) of Chap- 
ter 5, the absolute reverberation level is S + RL, so 
that the recognition level for reverberation is given by 
equation (17), 

R + M r = S + RL + M r . (18) 

3. The recognition level for noise is given by equa- 
tion (17) of Chapter 9, 

L + M n = N + D + 10 log w + M n . (19) 


These three equations show explicitly all the main 
factors affecting the range. 

The qualitative effect of these factors on the range 
is easily shown by reference to Figure 4. For example: 

Source Level S. A change in S will shift the curves 
of E and R + Mr by equal amounts, and will therefore 
not affect the reverberation-limited range. An increase 
in S will raise the E curves and thus increase the 
noise-limited range; a decrease will shorten it. 

Target Strength T. A change in T will affect E but 
leave R-\- Mr and L + M N unchanged. Thus increase 
in T will increase both noise- and reverberation-limited 
ranges. 

Transmission Loss H. As H increases, the echo- 
level curve drops, as shown by the change in going 
from curve 5 to curve 1, which corresponds to going 
from good transmission conditions to poorer. Thus 
increase in H will decrease both noise- and reverbera- 
tion-limited ranges. 

Reverberation Level RL. An overall increase in the 
reverberation level, caused, for example, by using a 
longer ping length, will tend to shorten reverbera- 
tion-limited ranges. It is worth emphasizing that, 
to a first approximation, the reverberation level is 
independent of thermal conditions. 

Recognition Differential M. For both noise and 
reverberation an increase in the recognition differ- 
ential effectively increases the background and there- 
fore shortens the range. 

The above parameters are not independent. One 
example, concerning source strength, has already 
been discussed. Two others are of particular interest. 

1. Effect of ping length r 0 . An increase in r 0 
increases RL proportionately ; according to Figure 2, 
however, it decreases Mr, at least in a region of 
considerable practical interest (30 to 200 msec). 
These two effects offset each other in equation (18) 
and leave R + Mr almost unchanged. Changing ping 
length, between 30 and 200 msec, therefore does not 
greatly affect reverberation-limited ranges. It should be 
pointed out, however, that since this involves Mr, 
the recognition differential for aural detection, this 
statement will require modification for other modes 
of portrayal. There is good evidence that with cer- 
tain methods of visual presentation, a decrease of 
ping length increases the reverberation-limited range. 
The effect of ping length on target strength has been 
discussed in Chapter 8, and will also have an in- 
fluence on the maximum range. 

2. Effect of target speed and aspect. The target 
strength T is high for beam aspect and low for bow 


198 


MAXIMUM ECHO RANGES WHEN REVERBERATION IS LIMITING 


or stern aspect. If the target is not moving, there- 
fore, the echo will be weaker, and both noise- and 
reverberation-limited ranges will be shorter for stern 
or bow aspects than for beam aspect. 

If the target is moving, however, doppler effect 
will be present for the stern and bow echoes and will 
decrease Mr, thereby lowering R + Mr and increas- 
ing the reverberation-limited range. At beam aspect, 
of course, there will be no doppler effect and the 
range will be unchanged. a The noise-limited ranges 
will, of course, be independent of the target speed, 
since M N is unchanged by doppler effect. 

The net result is that, with increasing target speed 
and any aspect except beam aspect, the reverbera- 
tion-limited range will be increased. Reverberation- 
limited ranges at beam aspect or noise-limited ranges 
at any aspect will be theoretically unaffected by 
target speed. 

10.4 2 Calculation of the 

Maximum Range 

To illustrate the method of calculating maximum 
ranges, three cases will be considered, corresponding 
to those in Chapter 9. It will be assumed that stand- 
ard 24-kc echo-ranging gear is being used in deep 
water, that the ping length is 100 msec, that the 
receiver has a wide-band ( w = 1,000 c) response, and 
that aural detection is employed. The values of the 
parameters S, T, Mr are given in Table 1. The same 


Table 1. Values of various parameters used in calcu- 
lating reverberation-limited ranges. 



Unfavorable 

case 

(db) 

Average 

case 

(db) 

Favorable 

case 

(db) 

s 

110 

110 

110 

T 

5 

15 

25 

Mr 

6 

-4 

-4 


values of S and T are used as in Chapter 9, the values 
of 5 db, 15 db, 25 db for T representing stern or bow, 
quarter, and beam aspect, respectively. For Mr the 
value of 6 db in the unfavorable case corresponds to 
no doppler; taken with the value of T = 5 db, the 

a This sentence is based on a very simple theory. Experi- 
mental evidence on the effect of target motion on the intensity 
of echoes from the beam aspect is puzzling and conflicting. 
The observed effects have been large on some occasions, but 
not always in the same direction. Further experimental work 
on this problem is urgently needed. 


combination represents a submarine dead in the 
water at stern aspect, a decidedly unfavorable situa- 
tion. For the average case Mr = — 4 db corresponds 
to slight doppler and, with T = 15 db, the combina- 
tion represents a creeping submarine under way at 
about 6 knots at quarter aspect. The favorable case 
T = 25 db and Mr— — 4 db corresponds to a fast- 
moving submarine seen about 10 degrees off the 
beam. A more favorable case would have been T = 15 
db and Mr = — 20 db, corresponding to high speed 
and quarter aspect; the case shown in Table 1 was 
taken in order to retain the large value of T = 25 
used in Chapter 9. 

Using the values of S and T in Table 1 for the 
average case, together with the same values of H{r) 
as were used in Figure 11 of Chapter 9, the E curves 
of Figure 4 were constructed. The R + Mr curve was 
obtained from the average for deep water given in 
Chapter 5 (curve 4, Figure 34). 

The recognition level for noise L-\-Mn corresponds 
to the average case used in Chapter 9 ; the values of 
the parameters assumed for all three cases are shown 
in Table 2. 


Table 2. Values of parameters used in calculating 
noise-limited ranges (from Chapter 9). 


Unfavorable 

case 

(db) 

Average 

case 

(db) 

Favorable 

case 

(db) 

N 

-30 

-45 

-60 

D 

-23 

-23 

-23 

m n 

- 3 

-13 

-23 

10 log w 

30 

30 

30 

Recognition 
level for noise 

-26 

-51 

-76 


The reverberation- and noise-limited ranges for 
the average case were read from Figure 4 and are 
shown in Tables 3 and 4, together with the corres- 
ponding values for the other two cases, determined 


Table 3. Estimates of maximum range (reverberation- 
limited). 


Thermal 

condition 

Unfavorable 

case 

(yd) 

Average 

case 

(yd) 

Favorable 

case 

(yd) 

1 

300 

400 

500 

2 

550 

800 

1,000 

3 

900 

1,400 

2,000 

4 

2,500 

5,000 


5 





MAXIMUM ECHO RANGES WHEN REVERBERATION IS LIMITING 


199 


Table 4. Estimates of maximum range (noise-limited). 


Thermal 

condition 

Unfavorable 
case 
(yd) ' 

Average 

case 

(yd) 

Favorable 

case 

(yd) 

1 

40b 

700 

1,500 

2 

700 

1,100 

2,100 

3 

900 

2,000 

3,000 

4 

1,400 

3,200 

5,600 

5 

1,700 

4,200 

7,400 


in a similar manner. In general, these numerical data 
should be considered as illustrative of the calculations 
and should not be used for operational decisions. 

Comparison of Limiting Ranges for Noise and 
Reverberation 

In order to determine the maximum echo range 
in a given situation, the limiting ranges must be 
calculated for both noise and reverberation and the 


Table 5. Estimates of maximum range (noise- and 
reverberation-limited) . 


Thermal 

Unfavorable 

Average 

Favorable 

Masking 

condition 

case 

case 

case 

background 


(yd) 

(yd) 

(yd) 


1 

300 

400 

500 1 


2 

550 

800 

1,000 

) Reverberation 

3 

900 

1,400 

2,000 j 

I 

4 

1,400 

3,200 

5,600 1 

i Noise 

5 

1,700 

4,200 

7,400 J 


shorter of the two chosen. This has been done for 
the cases above; the results are shown in Table 5. 
It is also useful to consider the range at which 
R + M r crosses L + M N ; this is the range at which 
the masking background changes from reverberation 
to noise. For the average case shown in Figure 4 
this occurs at 2,700 yd. Inside this range the limiting 
ranges must therefore be determined from the re- 
verberation (Table 3); beyond this range they are 
determined by noise (Table 4). 


Chapter 11 

MISCELLANEOUS ECHO-RANGING APPLICATIONS 


n.i OPERATIONAL PLANNING 

T he discussions in the preceding chapters of 
Part II have dealt primarily with the production 
of the echo-ranging signal and the detection of the 
echo, without devoting particular attention to specific 
situations and the problems associated with them. 
The present chapter is devoted to discussing the 
attempts that are being made to cope with some of 
the special operational difficulties encountered in 
trying to obtain information by echo ranging and 
to apply such information to tactical problems. 

11.1.1 Search Operations 

Echo ranging is used by the Navy for a number 
of different purposes, not all of them necessarily con- 
nected with naval warfare; its use as an aid in 
antisubmarine warfare is only one application, al- 
though perhaps one of the most important and 
dramatic. To whatever use it may be put, success is 
conditioned by the systematic execution of a care- 
fully considered operational plan. Such a plan is 
based on consideration of the several functions that 
underwater echo ranging can successfully perform. 

1. To establish contact with the target by using 
sound. 

2. To maintain contact with the target and iden- 
tify it. 

3. To obtain accurate determinations of the range 
and bearing of the target. 

4. To determine the rate at which the range and 
the bearing are changing — the range rate and bearing 
rate. 

Each of the last three of these functions succes- 
sively depends on the preceding ones. 

The discussion will fulfill its purpose if we restrict 
it to the application of echo ranging to search opera- 
tions in antisubmarine warfare prosecuted by a 
surface vessel. 

Employing the terminology of antisubmarine war- 
fare, in a search operation three different missions 
can be assigned to the surface vessel or squadron. 

Hunt: to find as many enemy submarines as 
possible, having little or no information as to their 
position at any earlier time. 


Location: to find a specific enemy submarine whose 
position at an earlier time is known with reasonable 
accuracy. 

Screen: to establish a zone (the screen) around a 
friendly area (a shipping lane or a moving convoy) 
such that all enemy submarines must pass through 
the screen in order to attack, and then to detect all 
enemy submarines while they are in the screen. 

There are a number of differences between these 
three assignments. “Hunt” and “location” missions 
are offensive, and the submarine may be expected 
to use evasive maneuvers. The “screen” operation 
is defensive, and its objective, the prevention of a 
successful attack, will be partially achieved if the 
submarine is forced to use evasive tactics. 

The success of these missions obviously depends 
in the first place on the probability of establishing 
sonar contact, that is, on the probability that when 
a ping is transmitted a recognizable echo will be 
returned. Intelligent operational plans can be worked 
out, therefore, only if all the factors affecting this 
probability are known and their effects evaluated. 
Some of these are intuitively apparent, e.g., in the 
hunt operation, success may be equally probable if 
one searches a wide area superficially or a smaller 
area intensively. In the location operation, success 
is assured if the echo-ranging vessel has sufficient 
speed to make an exhaustive search of a sufficiently 
large but limited area; provided, of course, that the 
self-noise at the high speed does not render the sonar 
inoperative. 

The effects of the other factors are not easy to 
evaluate. It will help to indicate the scope of the 
problem if we list the most important of these at 
this time. 

1. The range of the target. 

2. Its bearing deviation, i.e., the difference be- 
tween its actual bearing and the projector heading 
(see Section 11.2.1). 

3. Its relative bearing. 

4. Its depth. 

5. Its target strength. 

6. The prevailing sound conditions. 

7. The speed of the echo-ranging vessel. 

Some of these factors have been discussed fully 
in the previous chapters. The problem of bringing the 


200 


OPERATIONAL PLANNING 


201 


sonar into such a position as to insure a high proba- 
bility of obtaining echoes resolves itself into an 
analysis of the cumulative effect of all the factors. A 
large number of rules have been formulated, based 
on experience and a small amount of theoretical 
analysis. 1 However, no complete analysis of the 
problem has been made. Further work, experimental 
as well as theoretical, is needed. 

In this section, a few general and qualitative 
remarks will be submitted, suggesting the type of 
theoretical analysis referred to. It will be assumed 
that adequate data is available on the last four 
factors listed, and the dependence of the probability 
of establishing sonar contact on the range and bear- 
ing of the target only will be examined. 

11.1.2 The Probability of Detection — 

Single Ping 

Assume that a target is in the neighborhood of a 
sonar and that a single ping is transmitted. The 
dependence of the detection probability can con- 
veniently be exhibited on a contour map, like the 
one shown in Figure 1. It should be clearly under- 
stood that this figure is entirely schematic and is 
presented merely to illustrate the discussion of gen- 
eral principles. It does not represent the facts of 
any actual situation. 

The position of the echo-ranging sonar is indicated 
at the bottom of the figure. If the target is situated 
on a given contour, the number shown on the contour 
designates the probability of detection. For example, 
if a target is on the 60 per cent contour, a single ping 
will return a recognizable echo 60 per cent of the 
time. If the target is inside the 60 per cent contour, 
this probability will be greater. These numbers are 
called the detection probability. 

For all search operations, it is important that the 
area of each contour be as large as possible. It is also 
desirable that the maximum value of the detection 
probability be large. In order to obtain a single 
number that will describe the contour diagram, the 
areas between two adjacent contours may be multi- 
plied by the average value of the detection proba- 
bility, and the various products thus obtained added. 
The result is called the effective search area of a 
single ping. For example, the area between the 30 
and 40 per cent contour is measured and this quan- 
tity multiplied by 35 per cent, the average proba- 
bility in the area; then the process is repeated for all 



Figure 1 . Contour map showing detection probability 
of a stationary target using a stationary sonar. This 
figure is entirely schematic and is presented merely to 
illustrate the discussion of general principles. 

the zones, and the sum of the individual products 
computed. 

In order to obtain a larger area, the beam width 
could be increased. However, that might make the 
bearing determination less accurate, and thus the 
gain of one advantage would cause the loss of an- 
other. In the design of an all-purpose pinging sonar 
the various requirements must be carefully balanced 
against each other. 

n . 1.3 The Probability of Detection — 
Successive Pings 

In practice, surface vessels do not rely on a single 
ping for detection, although the tactical situation 


202 


MISCELLANEOUS ECHO-RANGING APPLICATIONS 


may force a submarine to do so. The analysis of the 
advantage of repeated pings in operational practice 
is complex; only a few major principles can be 
discussed here. 

The simplest case is that both sonar and target 
are at rest, and that two pings are sent out. Then it 
is possible that an echo will be recognized (1) on 
both of the pings, (2) on either of the pings, and 
(3) on neither of the pings. 

Let Wi be the probability that a single ping would 
return a recognizable echo for the given position of 
the target. Then the probability that the echo would 
not be detected is evidently 

l-wi. ( 1 ) 

Let us assume that the detection probability for the 
second ping is the same as if the first had not been 
transmitted. This is not likely, for the operator may 
have been doubtful of the echo from the first ping 
and may have ignored it, but a doubtful echo from 
the second ping will, under these conditions, be very 
apt to be considered certain. This is especially true 
if a range recorder is used and becomes an increas- 
ingly important effect as the number of pings in- 
creases. However, for simplicity, such memory and 
comparison effects will be ignored. 

The probability that the second echo will not be 
detected is thus also 

1 — Wi. 

The probability that neither of the two echoes 
will be detected is the product of the two proba- 
bilities, namely, 

(l-wi) 2 . (2) 

Hence the probability that at least one of the two 
echoes will be detected is 

w 2 = 1 — (1 — wi) 2 . (3) 

In view of the foregoing remarks, this value is apt 
to be too small. 

If n pings are transmitted, the detection proba- 
bility is 

w„ = 1 - (1 - wi) n . (4) 

Graphs of this equation for several values of n are 
shown in Figure 2. Even though these values, as has 
been said, are likely to be too low, the figure shows 
an increase of detection probability with each suc- 
cessive ping. This increase is most rapid for inter- 
mediate values of W\. If W\ > 0.5, five pings will 
make detection practically certain. 


w, 



Figure 2. Graphs of detection probability W n for n 
pings in terms of the detection probability IF of a 
single ping. 

n.i.4 Effect of Motion of 

Sonar and Target 

If the echo-ranging vessel is in motion, the cal- 
culation of the probability of making sonar contact 
with a target by using successive pings becomes 
more complicated. If the target is moving, still 
others arise. 

Let the target be on the contour w' of the first 
ping, and suppose that the motion of the sonar has 
resulted in placing it on the contour w" of the 
second ping. Then, by reasoning similar to that in 
the previous section, and again ignoring memory and 
comparison effects, the probability of detection by 
either of the two pings or by both is given by 

w — \ — (1 — ti/)(l — (5) 

Values of this function are tabulated in Table 1. 
Arbitrary values of w' are arranged in the top row, 
those of w" in the left-hand column, and the cor- 
responding values of w are found in the body of the 
table. For example, suppose that when the first ping 
is transmitted the target is on the 60 per cent con- 
tour, and that the motion of the sonar has resulted 
in placing it on the 50 per cent contour for the 
second ping. Then w' = 0.6, w" = 0.5, and from the 
table, w = 0.8. 

Table 1 can be used to construct a contour map 
similar to Figure 1 . Such a map is shown in Figure 3. 


OPERATIONAL PLANNING 


203 



© FIRST 
POSITION 

SONAR MOVES- TARGET STATIONARY 

Figure 3. Contour map of detection probability, 
similar to Figure 1, but considering the sonar to be in 
motion while the target is stationary. This figure should 
be compared with Figure 1. 


Table 1. Detection probability for two pings — moving 
sonar, stationary target. 


\ tl / 

0.1 

o !2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

0.1 

0.19 

0.28 

0.37 

0.46 

0.55 

0.64 

0.73 

0.82 

0.91 

0.2 


0.36 

0.44 

0.52 

0.60 

0.68 

0.76 

0.84 

0.92 

0.3 



0.51 

0.58 

0.65 

0.72 

0.79 

0.86 

0.93 

0.4 




0.64 

0.70 

0.76 

0.82 

0.88 

0.94 

0.5 





0.75 

0.80 

0.85 

0.90 

0.95 

0.6 






0.84 

0.88 

0.92 

0.96 

0.7 







0.91 

0.94 

0.97 

0.8 








0.96 

0.98 

0.9 









0.99 


The two successive positions of the sonar are shown 
at the bottom. It is assumed that the detection 
probability of each ping is identical with that dia- 


grammed in Figure 1, and that the pings were 
transmitted with the same projector heading. The 
motion of the projector between pings has been 
greatly exaggerated for purposes of illustration. 

Comparison with Figure 1 shows that each contour, 
e.g., the 50 per cent contour, has greatly expanded, 
and encloses more than twice the area of the same* 
contour for a single ping. Moreover, the maximum 
value of the detection probability has increased from 
75 per cent for the single ping to nearly 90 per cent 
for the two pings. Consequently, the effective search 
area of the two pings is more than doubled. 

The amount by which the effective search area of 
the overlapping pair exceeds twice the area of a single 
ping has been exaggerated by the exaggerated mo- 
tion of the sonar. In practice it will be somewhat 
less than is shown, but the effect will still be ap- 
preciable. In practice, also, more than two over- 
lapping pings will be used, and the effect is in- 
creased by this. / 

The possible motion of the target will have a rather 
different effect than that of the sonar. To see this, 
suppose that the target was actually detected at a 
certain point P at time to, and that at a later time t 
it is necessary to estimate its position. In order to 
illustrate the principles involved, suppose that be- 
tween to and t no further pings were sent out, and 
that the direction and speed of the target’s motion 
is unknown. Then it is possible to estimate only its 
speed, not its direction. It will be possible to draw 
probability contours, giving the probability that the 
target is at any given point at time t. These will be 
circles with centers at the point P. The radii of the 
various contours will depend on the probability that 
the target moves with the given speed. As the time 
interval t — 1 0 increases, these radii will increase, 
since the unknown motion of the target has more 
time to have its effect. 

These same considerations can be applied to the 
time interval between pings. If the ping was sent 
out at time to, Figure 1 will show the probability 
that, if the target is at a given place, it was detected. 
At a later time t, but before the next ping, the target 
may have moved. Consequently, Figure 1 does not 
show the probability that, if the target is at a given 
place at this later time, it would have been detected 
at the earlier time to. But it is possible in principle to 
work out the contours for this “prior-detection” 
probability. The effect of the unknown motion of 
the target will be to cause the contours of high 
probability to shrink as t increases. This is shown 


204 


MISCELLANEOUS ECHO-RANGING APPLICATIONS 




©B 


SONAR STATIONARY- TARGET IN MOTION 

Figure 4. Contour maps of detection probability, sim- 
ilar to Figures 1 and 3, but considering the target to be 
in motion while the sonar is assumed to be stationary; 

(A) this figure shows the change that has been brought 
about in Figure 1 after a certain interval of time; (B) 
this figure shows the change in Figure 1 after twice 
the interval. 

schematically by Figure 4 for two successive values 
of t. 

If several pings are sent out, it is these shrunken 
prior-detection contours that must be combined as 
explained in connection with Figure 3. The result of 
such a succession of pings is shown schematically in 
Figure 5. This represents the state of affairs at the 
time the echoes from the third ping are being re- 
ceived, and the contours show the probability that, 
if the target is then at a given point, it would have 
been detected either then or earlier. 



© 

© 

SONAR AND TARGET IN MOTION 

Figure 5. Probability contours for three successive 
pings, allowing for the motion of both target and echo- 
ranging vessel. 

The motion of the sonar and target have been 
exaggerated to emphasize the important points. It 
will be noted that, because of the unknown motion 
of the target, the 80 per cent contour of Figure 5 has 
a much smaller area than the 80 per cent contour 
of Figure 3 — and this despite the fact that the latter 
is based on three pings, the former on only two. 

n .2 TARGET BEARING 

The foregoing considerations of the probability of 
establishing sonar contact have been restricted to 
simple conditions. In general, the possibility of tak- 
ing action against a target in a given area depends 
not only on how completely the area can be searched 
in a short time, but also on the ability of the operator 



TARGET BEARING 


205 


to maintain sonar contact with the target once he 
has contacted it. The first of these requirements 
makes it desirable to design the sonar so that the 
search area of the ping is large. The second require- 
ment will be seen to be in some conflict with the first. 
Various special devices have been designed to avoid 
this conflict. These will be discussed after a prelim- 
inary examination of the operational problem in 
terms of the simplest sonar. 

11.2.1 Maintaining Contact 

After the signal has been transmitted, the sonar 
operator is on the alert for a sound contact with the 
target, i.e., a break in the background reverberation 
or noise, either as he listens to the sound from the 
loudspeaker or watches the chemical range recorder. 
(A specimen of a record from the latter is reproduced 
in Figure 19 of Chapter 8.) Having made a contact, 
his chief concern is to maintain it. 

This is difficult with ordinary sonar gear. The 
target may move out of the sound beam, either to 
the right or to the left. Because of the relatively long 
interval between echoes, the uncertainty as to the 
direction in which the beam should be rotated is 
serious. 

Bearing Deviation 

The target bearing is the direction of the line joining 
the projector to the center of the target and is not 
necessarily given by the projector heading, which is 
the direction of the axis of the sound beam. Because 
of the width of the sound beam, an echo may be 
received even when the axis does not bear on the 
center of the target (say, the conning tower, in the 
case of a submarine). Thus the target bearing and 
projector heading may not coincide. The difference 
between them is called the bearing deviation. When 
the bearing deviation becomes greater than a 
certain amount, the echoes become too weak to be 
heard. 

The projector is under the sonar operator’s con- 
trol, and thus the projector heading is known. The 
conning officer, however, wishes to know the target 
bearing. If the bearing deviation were small, it could 
be ignored. Unfortunately, every attempt to reduce 
it will increase the probability that the target may 
move out of the sound beam, and increase the ser- 
iousness of the uncertainty mentioned above. Thus 


every solution must be a compromise between con- 
flicting requirements. 

It is not only the beam pattern of the projector 
and the target width that affect the possible magni- 
tude of the bearing deviation ; the echo level and the 
level of background noise and reverberation are also 
instrumental. If reverberation is limiting, the possible 
deviation also depends on the doppler shift of the 
echo. For present purposes, it is not necessary to 
consider these matters in detail, but the principles 
explained in the previous chapters would suffice for 
their discussion. 

Crossing the Target 

The earliest solution of these problems was the 
operation known as crossing the target. In this opera- 
tion, the projector heading is systematically changed 
more rapidly than the target bearing changes. When 
the sound beam leaves the target, the projector 
motion is reversed, and continued until the sound 
beam leaves the target on the other side. This elim- 
inates the uncertainty mentioned above. Whenever 
no echo is obtained, the operator knows on which 
side of the beam he will find the target. The two 
limiting projector headings thus obtained are called 
cut-ons. The average of two successive cut-ons is 
taken as the best approximation to the target 
bearing. 

While the procedure is practicable, it has many 
disadvantages. The original echo may have come in 
on either half of the main beam. If the sonar operator 
begins to cross the target in the wrong direction, he 
risks losing contact . Moreover, it is time consuming, 
for it requires at least four, and often more, pings to 
obtain one value of the target bearing ; hence before 
this value is known to the sonar operator, the target 
may have moved, rendering the information more 
or less obsolete. 

n.2.2 Multiple Hydrophones and 
Split Transducers 

Modern solutions of these problems all involve 
the use of two hydrophones, and in principle, more 
than two could be used. The two hydrophones are 
often constructed in semicircular shape and of such 
dimensions that they can be mounted in the same 
space as the older circular transducers. Moreover, 
by changing electric connections before transmission, 




206 


MISCELLANEOUS ECHO-RANGING APPLICATIONS 



Figure 6. Diagram showing three successive stages in 
the passage of a plane wave front from the target to a 
transducer having two hydrophones (marked 1 and 2) 
spaced a unit apart. 

the projected sound beam can be made identical 
with that of the older circular transducer. Such pairs 
are called split transducers. 

The physical principles involved can most easily 
be explained by considering a pair of identical 



PHASE 

LAG 

CIRCUIT 


L' e 


- 4 ^*. 

C i 

Figure 7. Schematic diagram of circuit containing 
phase lag circuit, showing how a desired phase differ- 
ence between the currents from the two hydrophones 
is obtained. 



Figure 8. Graph of the three currents C i, C 2 , and CV, 
of Figure 7, plotted against the phase angle c ct, and 
showing the phase differences /S and /3 — 6 of Figure 7. 


hydrophones, mounted a distance a apart, with their 
acoustic axes parallel to each other and perpendicular 
to the line joining the two hydrophones. The general 
arrangement is shown schematically in Figures 6 
and 7. It is assumed that the pattern of the two 
hydrophones consists of a single broad lobe, as shown 
by the dotted line of Figure 9. 

Let an echo or other single-frequency sound be 
incident on the hydrophones from a direction that 
makes the angle a with the acoustic axes. Each 
wave will then reach the hydrophone closest to the 
target before it reaches the other, and the alternating 
currents generated by them will not be in phase. 
Under the circumstances shown in Figure 6, the 
current for No. 2 will be in advance of that from 
No. 1. This is shown in Figure 8, curves A and B. 
The phase angle jS can be calculated as follows : after 
reaching hydrophone No. 2, the wave must travel 
a distance l before reaching No. 1. This distance is 

1 = a sin a. (6) 


This is l/\ wavelengths, and since one wavelength is 
equivalent to a phase change of 360 degrees, the 
angle 13 will be given by 


/3 = 360 



sin a. 


(7) 


If the current generated by No. 1 is given by 

Ci = C(a) cos wt, (8) 



TARGET BEARING 


207 


o’ 



Figure 9. Graph of equation (13) for a/\ — 4, 0 = 90 
degrees. Note that as a result of the phase shift the 
single broad lobe of each hydrophone, indicated by 
the dotted curve, has been broken up into a number of 
narrower lobes (solid curves) ; also, that the axis of the 
main lobe has been displaced. The “lobe angles” are 
the angles at which the new beam patterns are tangent 
to the original ones. 

then that from No. 2 will be 

C 2 = C (a) cos (a )t -f- 0) . (9) 

The function C( a) is determined by the directivity 
pattern of the separate hydrophones (dotted curve, 
Figure 9). The graphs of the two currents C i and C 2 
are shown in Figures 8 A and B. 

If the current from hydrophone No. 1 is passed 
through a phase shifting network, the phase shift /3 
can be altered by any desired amount, say 0. This 
results in the current 

C' 2 = C( a) cos (c ot + p-d), (10) 

shown graphically in Figure 8C. The circuit is shown 
schematically in Figure 7, and the vector diagrams 
indicate the relation between the three currents. If 
Ci and C' 2 are combined, the resulting current will 
be a 

C = C\-\r C '2 = C (a) [cos (coQ + cos (<o£ + 0 — 0)] (11) 

Ci+C'.» = 2C(a) cosi(/3 — 0) cos [coZ + J(/3 — 0)]. (12) 

The level of the electrical output is thus 

L = 20 log [2C(a)] + 20 log cos [J(0 — 0)]. 

a In deriving the equation for C , use has been made of the 
trigonometric formula 

cos A + cos B = 2 cos \{A + B ) cos £(A — B). 


OX**") 



Figure 10. Values of the lobe angles, shown in Figure 

9, as a function of \/a and n, the order of the lobe. 

The first term of this expression is essentially the 
directivity pattern of the individual hydrophones. 
The second term also depends on the direction a 
from which the sound comes, since 0 depends on a. 

The graphs of the resultant level L, for the case 
(a/X) =4, 0 = 90 degrees, is shown by the solid line 
of Figure 4. It is seen that, as a result of connecting 
the two hydrophones together, the single broad lobe 
of each has been changed into a number of narrower 
lobes. 

The axis of the new main lobe does not coincide 
with that of the original lobe, nor are the side lobes 
symmetrically located. This is a result of the phase 
shifting network. Figure 10 can be used to calculate 
the positions of the lobes for any value of the quan- 
tities 0, X/a, and n, the order of the lobe. 

In this graph, the lobe angle is the point at which 
the new and the original beam patterns are tangent 
(see Figure 4) and the integer n is zero for the main 
lobe, ± 1 for the two lobes on either side, ± 2 for the 
pair of second lobes, etc. The phase lag 0 is to be 
measured in degrees. 

11.2.3 Bearing Deviation Indication 

Various devices employing the split transducer 
principles have been designed. They are known by 
various names: bearing deviation indicators, vector 
bearing indicators, and phase-actuated locators are 
several designations. They all use a split projector 
and differ only in detail. 1 


208 


MISCELLANEOUS ECHO-RANGING APPLICATIONS 


SPLIT TRANSDUCER 




SCHEMATIC OF BDI SYSTEM 

Figure 11 . Schematic of BDI system. 



Figure 12. Shift of main lobe of beam pattern in BDI. 
The center pattern shows the normal beam of a circular 
diaphragm. For transmission the two halves of the 
transducer plate are connected together and this pattern 
is projected. The two side figures show the beam pat- 
terns for the two halves of the circuit shown in Fig- 
ure 11. 

For transmission, the two semicircular parts are 
connected so as to produce the normal beam of a 



Figure 13. Graph of currents from the two channels 
as a function of bearing deviation. 


circular diaphragm illustrated by the center curve 
of Figure 12. For reception, the two halves are con- 
nected as shown in Figure 11. It will be noted that 
there are two symmetric output channels. The con- 
nections of the right channel are the same as for the 
pair of hydrophones in Figure 7. The connections of 
the left channel differ only in that the phase lag is 
introduced into the output of No. 1 rather than No. 2. 
The beam pattern for the right channel thus has its 
main lobe deflected to the right, as shown by the 



Figure 14. Graph of the difference between the cur- 
rents from the two channels as a function of bearing 
deviation. 


right-hand curve of Figure 12; the main lobe of the 
left channel, on the other hand, is to the left. This is 
perhaps shown more clearly in the rectangular co- 
ordinate system used in Figure 13. The ordinates 
are the currents out of the two channels. In practice, 
these currents are rectified, as indicated in Figure 
13; the diodes are shown in Figure 11. 

The rectified output currents may be used for 
various purposes. They are commonly connected to 



TARGET BEARING 


209 


TARGET- 








▼ 


Submarine echo 




Figure 15. Diagrams illustrating BDI. (A) Target to the left of the projector heading causes the dot on the oscillo- 
scope to be deflected to the left; (B) target on dead center causes a brightening of the spot; (C) target to right of 
projector heading causes the dot to be deflected to the right; (D) echoes must be distinguished from reverberation. 
For this purpose the visual perception is supplemented by listening to a loudspeaker. 


an indicator ( cathode-ray oscillograph [CRO]) in such 
a way that its deflection is proportional to the differ- 
ence between the currents in the two channels. This 
difference is plotted as a function of bearing devia- 
tion in Figure 14. It is seen that, if the latter is not 
too great, the difference current is proportional to the 
bearing deviations. It is positive when the deviation 
is to the right, negative when to the left. Thus the 
indicator can (in principle at least) be calibrated in 
terms of bearing deviation. Confusion can occur if 
the deviation is greater than the limits set by the 
double arrow of Figure 14. 

11 . 2.4 The Standard BDI 

A device designed by the Harvard Underwater 
Sound Laboratory [HUSL] according to the prin- 
ciples just discussed has become standard equipment 
in the Navy. It is known as the hearing deviation 
indicator [BDI]. The QGB stack shown in Figure 19 
of Chapter 7 has the BDI on its sloping panel. 

The BDI provides a visual indication of the sound 


incident on the transducer. When the transducer is 
trained on the exact center of the source (Figure 
15B), the incident sound strikes both halves of the 
diaphragm simultaneously; this is indicated by a 
brightening of the luminous trace on the screen of 
the CRO. When the transducer is trained slightly 
off the center of the target (Figures 15A and C), the 
incident sound waves strike one of the transducer 
halves before the other. This causes the brightened 
trace on the screen to be deflected in the direction of 
the half on which the sound first impinges; a de- 
flection to the left thus would show that the source 
was to the left of the transducer bearing, and that 
the operator must train left to get a dead-on bearing. 
Similarly, a deflection of the brightened spot to the 
right would indicate that the operator should train 
right. An accurate bearing can be obtained by 
getting both a right and a left deflection. 

Since the BDI reacts to all sound energy incident 
on the transducer, it must be used in conjunction 
with the loudspeaker in order to distinguish between 
echoes and reverberation, and also between echoes 
themselves, particularly between the echo from a 


210 


MISCELLANEOUS ECHO-RANGING APPLICATIONS 


submarine and that from its wake (see Figure 15D). 

The motion of the spot across the screen is con- 
trolled by the range indicator and is synchronized 
with it. It appears on the bottom of the screen at 
the beginning of the ping, and travels up the screen 
in the time required for the range indicator to make 
one revolution. Hence the spot can move at a rate 
corresponding to a range of 5,000 yd or to one of 
1,000 yd. In addition, a range selector switch is 
provided by which the operator can control the speed 
of the spot. It is evident that the position of the 
bright spot on the screen makes possible a quick 
estimate of the range of the target. 

The rather narrow deflection limits of the indi- 
cator make it desirable to employ a time-varied gain 
[TVG] control on the signal transmitted to the in- 
dicator. By this means it is possible to have low gain 
for the strong echoes from nearby targets and re- 
verberations that correspond to short time intervals 
after the emission of the ping, and progressively higher 
gains for the weaker echoes from distant targets. 

ii 3 SCANNING SONAR— PULSED 

TRANSMISSION 

The problem of rapidly searching a wide area led 
to the development of so-called scanning sonars. Two 
main kinds have been designed: one kind transmits 
short pulses of sound, the other kind a continuous 
signal of varying frequency. 

u.3.1 Objective of Pulsed Scanning 

Sonar 

The original methods of echo ranging all involve 
a short transmission of sound, followed by a longer 
period during which the sonar operator is alert for 
echoes. This period must be long enough so that no 
further echoes of any one ping can arrive after the 
next has been transmitted; otherwise the interpre- 
tation of the echoes would be uncertain. For example, 
if a target is located a mile away, over 2 sec are 
required for the echo of a given ping to be returned 
to the sonar. Thus, the number of echoes that can 
be obtained from a given target in a given time is 
strictly limited, and decreases as the range of the 
target increases. The corresponding problem in radar 
is much less serious because of the much greater 
velocity of radio waves. 


A second limitation is that because of its directivity, 
the sonar is, at a given moment, alert only to echoes 
from targets in a relatively narrow sector. This is 
particularly serious when many targets must be 
anticipated, as for instance, when sonar is used for 
navigation in a mine field. Under these conditions, 
the time consumed in training from one bearing to 
another might well be fatal. Even under less stren- 
uous conditions, it makes it difficult for the operator to 
be certain of the momentary situation on all bearings. 

The objective of the developments discussed in 
the present chapter is to utilize the necessary interval 
between pings to search the widest possible sector. 
In this way, the area searched per ping and the 
amount of information received per unit time will 
both be increased. 

h. 3.2 General Principles 

This objective can be achieved by flooding the 
search area by pulses from a transmitter that is non- 
directional in a horizontal plane, thus transmitting 
energy to all bearings with each pulse. The projector 
need not transmit energy along rays that are much 
inclined to the horizontal, however. The echoes are 
received on a rapidly rotating, sharply directional 
hydrophone. At any instant the outgoing train of 
waves will thus occupy a ring-shaped region, as 
shown in Figure 16, marked “wave train.” The radius 
of this ring increases with the velocity of sound. 
Echoes, on the other hand, can be returned to the 
hydrophone, at a given instant, only from a small 
region — the “active volume” defined in Chapter 5, 
and shown in the figure crosshatched — determined 
by the ping length r 0 and the angular width of the 
beam. This region is located at half the range of the 
wave train, and has half the extent of the latter in 
range ; its width, or extent in bearing, is limited by the 
directionality of the hydrophone. Since the latter is 
rotating, the active region will describe a spiral path. 
The radius of the spiral increases with half the velocity 
of sound; the speed of the active volume in the spiral 
path will, of course, be much greater than this. 

In order that every possible target should at some 
time be encountered by the active region, the hydro- 
phone must not be rotated too slowly. Otherwise the 
condition illustrated in Figure 17 results: there is a 
dead area between the rings of the spiral traced out 
by the active volume. This dead area is shown un- 
shaded and echoes from targets in it will not be 


SCANNING SONAR PULSED TRANSMISSION 


211 



Figure 16. Diagram of wave train and active region, 
for the case of a rotating hydrophone. The sound at 
a given instant occupies the ring-shaped shaded region, 
marked “wave train.” The radius of this ring increases 
with the velocity of sound. Echoes can be received to 
the hydrophone, at a given instant, only from the 
“active volume,” shown cross-hatched, determined by 
the ping length, r 0 , and the angular width of the beam. 
The active region describes a spiral path. 


received. The pitch s of the spiral, in this case, is 
greater than the ping length r 0 . If the hydrophone 
makes one revolution during the ping duration t Q of 
the signal, s will equal r 0 , and there will be no dead 
areas. If t 0 is expressed in milliseconds and r 0 in yards, 
r 0 = 0.8^o, since t Q = 2 r 0 /c sec. 

Conversely, if the rotation of the hydrophone is 
fixed, the ping must have a duration of at least one 
revolution. Thus, if the hydrophone is rotated at 
1,800 rpm, one revolution takes place in 33.3 msec, 
and consequently, the ping length must be greater 
than 0.8 X 33.3 = 26.7 yd. A value of r 0 = 30.0 yd 
would be safe if the ping is truly rectangular. 

A consequence of the rotation of the hydrophone 
is that the echo will not have the same duration as 
the transmitted pulse. The echo will be received only 
while the hydrophone beam is passing over the 
target. If the effective width of the hydrophone beam 
is 6 degrees, the echo from a point target, i.e., a 
target smaller than the active area, will be received 



Figure 17. Diagram showing the result of rotating 
the hydrophone too slowly. There is a dead area be- 
tween the rings of the spiral traced out by the active 
volume — this area is shown unshaded. 

during 0/360 of a revolution. Taking 0=11 degrees 
and 1,800 rpm as an example, the duration of the 
echo will be approximately 1 msec. Expressed in 
yards, the echo length n is 0.8 yd. The echo length 
n must thus be distinguished from the ping length 
r 0 . In every case, n will be smaller than r 0 , and will 
be independent of the ping length, provided the 
latter is of the required order of magnitude, as ex- 
plained above. 

This shortness of the echo duration is a conse- 
quence of the increased velocity with which the 
active volume moves. In fact, it may be said that 
this increased velocity of the active region is the pri- 
mary characteristic of pulsed scanning sonar. 

The short duration of the echo, in its turn, has a 
number of consequences: 

1. Doppler discrimination will be much impaired 
(see Section 10.2). 

2. Since the spectrum of the short echo extends 
over many critical bandwidths of the ear, the ad- 
vantage of the ear over other methods of perception 
is lost (see Section 9.3.4). 

3. The pass band of the receiver must be at least 
wide enough to pass the short echo. This will involve 
increased noise levels (see Section 9.1). 

4. The level of the reverberation, being determined 
by the volume of the active region, will be compar- 


212 


MISCELLANEOUS ECHO-RANGING APPLICATIONS 


able to that of standard sonars transmitting pings 
of length r 0 (see Section 5.3.2) and thus greater than 
for pings of duration n. 

5. The coherence of the reverberation will be com- 
parable to that of sonars transmitting pings of length 
ri (see Section 5.3.6). 

All these effects will tend to reduce the maximum 
range obtainable on a given target unless compen- 
sated by a suitable device for detecting the echo or 
by the sixth effect: 

6. The target strength of an extended object is 
determined by the size of the active volume, and will 
therefore be that which is characteristic of standard 
sonars transmitting pings of length r 0 . 

11.3.3 Plan Position Indicators 

The high rate of rotation of the hydrophone makes 
it impossible for an operator to follow the changes 
in its heading with his unaided senses. This, together 
with effects 1 and 2 listed above, makes it necessary 
to use special devices to portray the echo and render 
the bearing and range of the target perceptible. These 
devices are called plan position indicators. 

The only device of this kind which is feasible for 
the high rates of rotation contemplated above is a 
persistent-screen cathode-ray oscilloscope. The spot 
of this scope is made to describe a spiral path in 
synchronism with the active area. The path of the 
spot on the screen is thus a map of the path of the 
active volume. The brightness of the spot is con- 
trolled by the intensity of the received sound, so 
that an echo will be seen as a brighter spot than the 
background of reverberation and noise. Because of 
the synchronization of the spot with the active vol- 
ume, the echo will appear at the proper range and 
relative bearing on the screen. 

If there are several targets in the field, these will 
be portrayed in their proper relative positions. If 
echoes are obtained from reefs or sand banks, these 
will appear on the screen as brightened areas. Thus 
scanning sonar with a plan position indicator pre- 
sents the operator with a complete map of the 
underwater situation. 

n.3.4 CR and ER Sonars 

In principle, the receiver of a scanning sonar could 
be a directional transducer rotated about a vertical 



Figure 18. Schematic diagram illustrating CR scan- 
ning sonar. The twelve hydrophones are connected 
each to a segment ( B ) of a stationary commutator. 
These are contacted by a rotating brush (A) which 
connects five or six hydrophones to the receiver at any 
one time. In practice, the power is transmitted from 
commutator to brush by capacitive coupling rather 
than by actual contact. The receiving pattern of the 
array is markedly directional and rotates with the 
brush A. This is indicated at C. 

axis. However, the high speeds required make this 
impracticable. 

The same result can be accomplished by using a 
ring of stationary hydrophones and connecting the 
receiver to them in succession by means of a com- 
mutator. This is shown in Figure 18, twelve hydro- 
phones being shown. Each of these is connected to 
one segment B of a stationary commutator. These 
segments are contacted by a rotating brush A, which 
connects five or six hydrophones to the receiver at 
any one time. As the brush rotates, these are dis- 
connected in succession and replaced by others farther 
along the ring. The result is that the receiving pattern 
of the array is markedly directional, and rotates 
with the brush A . • 

Since sliding contacts would generate too much 
electrical noise, a small gap is provided between the 
moving brush A and the commutator segments, 
forming an electric condenser. The electrical power 
is thus transmitted by capacitative coupling, rather 
than by conduction. This does not entirely eliminate 



SCANNING SONAR PULSED TRANSMISSION 


213 


commutator noise, however. Scanning sonars oper- 
ated on this principle are often designated by the 
initials CR (for capacitative rotation of the beam). 

A second proposal for avoiding electric noise 
involves the elimination of all moving parts, and the 
use of electronic switches to perform the commuta- 
tion. The initials ER (electronic rotation) are applied 
to this system. 

11.3.5 Sector Scan Sonar 

The echo length resulting from the necessarily 
rapid motion of the active volume can be somewhat 
increased by scanning only a sector rather than the 
complete horizon. In this case the path of the active 
volume must be somewhat as shown in Figure 19, 
and its speed can be reduced. 

The oscillation of the receiver beam can be accom- 
plished by a modification of the principles already 
discussed in connection with the BDI. Several sta- 
tionary hydrophones are continuously connected to 
the receiver amplifier, each hydrophone having a 
phase shifting circuit interposed between it and the 
amplifier. The phase lags are so chosen that a sharp 
hydrophone pattern results, and they are varied, by 
electronic means, so that the axis of the beam oscil- 
lates with the required frequency. The basic principles 
that permit this to be accomplished have already 
been discussed in Section 11.1. 

A plan position indicator is also required for sector 
scanning, the CRO spot again tracing a synchronous 
map of the motion of the active region. 

n.3.6 Rotating Projectors 

One disadvantage of the pulsed scanning sonar is 
the relatively large power output that is required to 
obtain an adequate echo level. To insure this, the 
sound energy must be radiated in all directions at 
a level that must be at least as great as that which 
conventional sonars radiate in a narrow cone. An- 
other disadvantage is that the reverberation level is 
high out of all proportion to the echo length n. 

It might be supposed that this could be overcome 
by using a rotating directional projector and a non- 
directional hydrophone; but a moment’s reflection 
makes it apparent that this would make it impossible 
to determine the bearing of the target. The result 
achieved would not differ essentially from that ob- 



Figure 19. Schematic diagram illustrating the prin- 
ciple of scanning a sector rather than the complete 
horizon. 

tained by having both hydrophone and projector 
nondirectional and stationary. 

The possibility of rotating both projector and 
hydrophone presents itself. Detailed consideration of 
this proposal shows that the necessary output and 
the reverberation-echo ratio could both be reduced, 
but probably not by more than 10 db. It is doubtful 
whether this advantage would compensate for the 
additional complication of the gear. 

In general, the rotating projector contributes little 
to accomplishing the basic function of the pulsed 
scanning sonar, which is to increase the speed of the 
active region beyond its normal value of half the 
velocity of sound. Consequently, rotating projectors 
can be considered only in connection with refine- 
ments of the gear and not in connection with its 
basic design. 

It may be possible to abandon the basic principle 
of pulsed scanning sonar and to design useful systems 
operating on other principles and using rotating pro- 
jectors. For example, if a directional projector makes 
one complete revolution and transmits sound of 
constantly increasing frequency during that time, 
the bearing of a stationary target can be identified 
by the frequency of its echo. The pitch of the echo 
from a moving target, however, will be determined 
both by its bearing and speed. Thus the problem of 
correctly estimating both bearing and motion of a 
target becomes complex. Moreover, the own-doppler 
caused by the motion of the sonar through the water, 
will introduce complications. The theory of this type 


214 


MISCELLANEOUS ECHO-RANGING APPLICATIONS 


of sonar has not been carefully examined, but is 
somewhat similar to that of FM sonar, which will 
be discussed in the next section. 


11 4 SCANNING SONAR— CONTINUOUS 
TRANSMISSION 


n.4.1 Principle of FM Scanning Sonar 

It was pointed out earlier in this chapter that the 
long delay between the transmission of the signal 
and the reception of the echo, caused by the low 
velocity of sound, is a handicap in search operations. 
Pulsed scanning sonar, as has been seen, utilizes this 
delay to scan all bearings, thus effectively increasing 
the speed of the active area. 

The possibility of using the delay period to make 
other transmissions presents itself. Obviously, if 
this were done, it would be necessary to be able 
to associate a given echo with the particular signal 
that caused it. The idea can be illustrated very 
simply. 

Assuming that the maximum practical range is 
about 3,000 yd, the maximum time delay is about 4 
sec. Suppose that during these 4 sec eight pulses were 
transmitted at 3^-sec intervals, the frequency of each 
pulse differing from its predecessor by a stated amount. 
They might form the tones of the major diatonic 
scale. Then a musically inclined listener would be 
able, on hearing an echo, to state its pitch and thus 
identify the ping responsible for it, provided, of 
course, both source and target were stationary, as 
otherwise the doppler effect would alter the pitch of 
the echo. Some means would have to be provided 
for recording the time and projector heading for 
each ping, to enable the determination of range and 
bearing of the target. 

While this illustration is greatly oversimplified, it 
can serve as a point of departure for the discussion 
of a sonar that uses the principle. 

In practice it is simpler to change the frequency 
more or less continuously than by abrupt steps. The 
frequency is allowed to decrease at a constant rate 
for some seconds; when it approaches the lower limit 
of the pass band of the receiver, it is suddenly in- 
creased to its original value, and the constant rate 
of decrease begins again. The principle is explained 
by the time graph of the transmitted frequency 
shown as the solid curve in Figure 20 A. This kind of 




Figure 20. (A) Diagram illustrating the principle of 
FM sonar. The solid curve is the frequency-time graph 
of the “sawtooth” signal, the dotted curve that of the 
echo. The echo lags behind the signal by 2r/c sec; this 
causes a difference in the frequency / or /'. The time 
interval T is the sawtooth interval; (B) graph of the 
frequency difference as a function of time. 

transmitted signal is known as a “sawtooth.” The 
intensity of the transmitted sound is kept constant 
during the transmission. 

A target located in the sound beam will return a 
continuous echo and, if both the sonar and target 
are stationary, this echo will reproduce the constant 
frequency change of the transmitted signal. However, 
because of the time delay between transmission and 
echo, the sawtooth graph of the echo will lag behind 
that of the signal, as shown by the dotted line in 
Figure 20 A. During a portion of the sawtooth in- 
terval (indicated in the figure by T), the echo fre- 
quency will be less than the transmission frequency 
by a difference /'. During the remainder of the time 
T it will be greater by a difference /. This is further 
illustrated by Figure 20B, in which the difference in 
frequencies between signal and echo is plotted as a 
function of the time. The frequency difference / is 
seen to remain constant for relatively long periods, 
and then to jump suddenly to the value/'. 

It is possible to perform the subtraction of the 
frequencies, i.e., to determine/ or/', electrically, by 
applying the heterodyne principle : a voltage tapped 
from the transmitter is combined with the hydro- 




SCANNING SONAR CONTINUOUS TRANSMISSION 


215 


phone output in a heterodyne stage of the receiving 
amplifier. 

4 From either of these frequency differences / or /' 
the range can be determined ; the calculation is given 
below. 

Up to this point we have supposed that there is 
only one target in the sound beam. If there are more 
than one returning echoes, each echo will have its 
time graph of frequency, the displacement of which, 
relative to the graph of the signal, will depend on 
the range of the target. The output of the receiver 
will thus contain components of several frequencies, 
one pair of frequencies for each target in the sound 
field. This complex output must be analyzed into 
its components in order to determine the range of 
the several targets. 

The active region from which echoes are being 
received occupies the whole of the sound field. More- 
over, it is stationary if the projector and receiver 
headings are not changing. Thus the basic objective 
of continuous transmission sonar is to increase the 
size of the active region rather than. its speed. The 
method just outlined for accomplishing this has been 
called FM sonar. 

When used with stationary projector and hydro- 
phone, FM sonar is not a bearing scanning device. 
However, it can also be used with a nondirectional 
projector and rotating directional receiver, and then 
becomes a scanning sonar but of a different type from 
that described in Section 11.3. 

It is possible that other methods of increasing the 
size of the active area could be devised, but FM sonar 
is the only sonar of this class that has yet been built. 

n.4.2 The Parameters of FM Sonar 

The Relation Between Target Range and 
Echo Frequency 

How the frequency difference between the echo 
and the transmitted signal determines the range will 
be apparent from the following discussion and 
reference to Figure 20. 

The duration of one sawtooth is T sec. During 
this interval the frequency varies at a constant rate 
from F + s to F; s is called the sweep of the frequency. 
In one model, the QLA, F = 36 kc, and s = 12 kc. 
T is usually from 1 to 12 sec. 

The following relations exist between the several 
parameters : 


1. The constant rate of frequency decrease 
is s/T kc. 

2. The delay time for an echo from range r is 
2 r/c sec. 

3. In 2 r/c sec the frequency will therefore decrease 
by (2 r/c) (s/T) kc, and the frequency difference /, 
shown in Figure 20A, will be 

2r s 

/ = -- kc. (14) 

c T 

4. From equation (14), the range r is given by 

/ 

r = cT (15) 

2s 

5. The frequency difference / will be maintained 
for T — 2r/c sec. At the end of this interval, the 
transmitted signal has reached the bottom of the 
frequency sweep and returns to the top of the sweep. 
During a succeeding time interval equal to 2 r/c sec, 
the echo frequency will be less than the transmitted 
signal frequency by/' kc (see the figure), where 

r=s-f. (i6) 

If the sawtooth interval T is several times greater 
than the delay time of echoes from the maximum 
range, the frequency/ will be less than s/2, and the 
frequency/' greater than s/2. 

6. The duration of the frequency /' will be con- 
siderably less than the duration of the frequency /. 
Consequently, it is economical to ignore the fre- 
quency /' and concentrate on the determination of 
the frequency /. 

The Determination of / and r. 

From equation (15) it is evident that / must be 
known to determine r. This is done as follows: 

Suppose the heterodyned output (the hydrophone 
output mixed with a sample of the signal) is passed 
through a band-pass filter centered at / kc, and of a 
width w kc. This filter will then pass an echo only if 
its frequency lies within this band, namely, between 
f — w/2 and f+w/2. This is equivalent to saying 
that the sound energy admitted by this filter comes 
from a certain active area (see Figure 21) which will 
be a sector of a circular ring. By using a battery of 
such filters, a series of channels is established, each 
of which is constantly alert to echoes coming from a 
certain active area. The dimensions of the area cor- 
responding to a given filter are easily calculated. The 
greatest ranges from which the particular filter under 


216 


MISCELLANEOUS ECHO-RANGING APPLICATIONS 



CHANNEL I 

CHANNEL 2 

CHANNEL 3 

CHANNEL 4 

CHANNEL 5 

CHANNEL 6 

CHANNEL 7 


Figure 21. Active areas associated with the individual 
channels in FM sonar. 


consideration will accept an echo is, from equa- 
tion (15), 


cT 


f+hw 
2 8 


and the smallest range, 


cT 


f-jw 
2 8 


The radial extent r 0 of the area is the difference be- 
tween the two ranges, and thus 


r 0 = cT 


(17) 


The other dimension of the active area is determined 
by the range and the width of the hydrophone beam ; 
and from elementary geometry its mean value is the 
product of the mean range times the angular width 
of the beam expressed in radians. 

The dimensions of the active area are proportional 
to the sawtooth interval T and, insofar as they are 
determined by T, are under the operator’s control. 
For example, if T = 12 sec, s = 12 kc, and w = 35 c, 
then r 0 = 30 yd. Reducing the value of T to 1 sec 
would make r 0 = 2.5 yd. 

As has been remarked, each of the channels will 
be almost constantly alert to targets in the particular 



TARGET 


Figure 22. The geometry of depth determination. 
The range indicator shows the slant range R, the depth 
of the target below the projector is Y, and its horizontal 
range is X. Knowing the angle of tilt 0, the value of X 
and Y can be calculated from X = R cos 6, Y = R sin 0. 

area associated with it. These areas are indicated in 
Figure 21. The active area of each channel is sta- 
tionary, and by making the areas of adjacent channels 
overlap slightly, the whole sound field can be 
covered, as shown in the figure. 

Because of the exclusion of the frequencies/', each 
channel would normally be inert for a part of each 
sawtooth cycle. However, this fraction can be made 
as small as desired or can even be completely elim- 
inated by a recent ingenious development. 

Since the active areas are stationary, it might 
seem that the range could not be determined so 
precisely as is possible with pinging sonars. Actually, 
however, the precision is the same as for a ping 
length equal to r 0 . The quantity r 0 defined by equa- 
tion (17) can be called the effective ping length of 
FM sonar. 


Range and Bearing Indication 

The range is read on an oscilloscope with a per- 
sistent screen. The filters corresponding to the various 
mean ranges of the several channels are arranged so 
that their output lights up the oscilloscope trace at a 
point whose distance from the center is proportional 
to the frequency / and thus to the range. 

An additional device makes the bearing of the 
echo spot on the oscilloscope correspond to the 
hydrophone heading. Figure 22 is a diagram of the 
FM sonar screen. 

For complete details the reader is referred to the 
discussions presented in several previously published 
reports. 2 ,3,5, 6 

Echo Duration 

The duration of the echo will depend, in the first 
place, on whether or not the hydrophone is stationary 
or is being rotated. If the projector is nondirectional, 


SCANNING SONAR CONTINUOUS TRANSMISSION 


217 


then the echo in a stationary hydrophone will have 
a duration nearly equal to the sawtooth period T. If 
the hydrophone is rotated, the echo duration may 
be reduced, becoming equal to the time required for 
the hydrophone beam to sweep across the target. 
The rate of rotation can be made as small as is re- 
quired to obtain an echo of any desired duration less 
than T. In this respect FM sonar differs from the 
pulsed scanning sonars described previously. 

The rotation rate cannot be increased beyond a 
certain critical value, however. This limitation is a 
consequence of the use of filters, which require a 
finite time interval to respond fully to the echo. The 
minimum time interval depends on the width w of 
the filter, and must be greater than 1/w sec, if w is in 
cycles per second. 

Suppose the hydrophone is rotated at a rate of N 
rpm and that its beam width is 0 degrees. A complete 
revolution requires 1/N minutes = 60/iV sec. The 
beam occupies 0/360 of a revolution; thus the time 
required for it to sweep across a given point is 0/360 
times Q0/N=6/QN sec. Hence, it is necessary that 

0 1 
QN w 

from which it follows that N must be less than }/q6w. 

As an example, let 0=11 degrees and w = 35 c ; 
then N must be less than 65 rpm. The echo duration 
for 65 rpm is 29 msec; the echo length corresponding 
to this is 23 yd. If the rotation is slower, the echo 
length will be increased. 

n.4.3 The Doppler Range Error 

It is clear that, since FM sonar uses the frequency 
of the echo to determine the range of the target, the 
doppler shift resulting from a possible relative motion 
of sonar and target will introduce an error into the 
indicated range. The magnitude of this error must 
be evaluated. 

FM sonar is calibrated so as to indicate the range 
77 (/ for “indicated”) according to equation (15), 


cTf 



This is the correct range if the range of the target is 
not changing, but it is necessary to calculate the 
error in 77 caused by the doppler change of frequency 
when the range is opening or closing. 


In all echo-ranging operations, three instants of 
time must be considered. These are (1) t h the time 
at which the primary sound was transmitted from 
the projector; (2) tr, the time at which the echo was 
reflected from the target; and (3) t E , the time at 
which the echo was received. 

If there is any relative motion of sonar and target, 
the range will be different at these three times. Call 
the corresponding ranges r h r T , and te- In the case 
of pulsed sonar, the range indicated is always rr, 
regardless of the possible motion of sonar and target. 
The differences between r h rr, and r E are negligible. 
This can be quickly verified when it is remembered 
that a speed of 1 knot is equivalent to 0.56 yd per 
sec, so that a speed of 25 knots would involve an 
error of less than 50 yd in a range of about 3,000 yd. 

None of the three ranges just defined is the range 
indicated by FM sonar. This range 77 is defined by 
equation (15). In order to calculate 77 , one must 
distinguish between three supersonic frequencies. 

1. Fi, the frequency that was being transmitted 
at the time ti. 

2. F e , the frequency that was being transmitted 
at the time t E . 

3. F' e , the frequency of the echo that was being 
received at the time t E . 

The quantity / of equation (15) is obviously 
F'e ~ F e , hence 

r I = —(F'E-F E ). (18) 

2s 

Let us examine the frequencies F E and F' E more 
closely. To simplify the calculation, it may be as- 
sumed that the sonar is stationary. No error is 
introduced by this assumption provided v of equa- 
tion (20) is interpreted as the range rate. When the 
target reflects the sound, its range is rr, and the 
transmitted frequency at the time t E will have been 
reduced by (2 r T /c)(s/T). The possible motion of 
the target will not affect this quantity. Thus the 
frequency being emitted at the instant when the 
echo is received is given by 

2s 

F e = Fi ~ r T- (19) 

The frequency of the echo, on the other hand, is 
affected by the motion of the target. From the theory 
of the doppler effect, the value of F'e will approx- 
imately be 

F'e = F l ±- F h (20) 

c 


218 


MISCELLANEOUS ECHO-RANGING APPLICATIONS 


where v is the range rate of the target. Subtracting 
equation (19) from equation (20) we have 

2s 2v 

F'e — Fe = — -tt ± — F i , ( 21 ) 

cT c 

and substituting equation (21) into equation (18) 
gives 

vT 

ri — r T ± — Fi. (22) 

s 

The error in the indicated range is therefore pro- 
portional to the velocity of the target, and is zero 
only for stationary targets. 

As an example, let T = 12 sec, s = 12 kc, and 
Fi = 36 to 48 kc, then 

TFi 

= 36 to 48 sec. 

s 

The range error is thus the distance moved by the 
target in 36 to 48 sec, the larger error occurring when 
the sawtooth frequency Fi is high, the smaller when 
it is low. The distance traversed in 48 sec by a sub- 
marine at 10 knots is slightly over 200 yd. 

It should be noted that the error is also propor- 
tional to the sawtooth period. Thus if in the ex- 
ample, T had been 1 sec rather than 12, the range 
error would be the distance moved by the target in 
3 to 4 sec, about 20 yd at a speed of 10 knots. 

It may also be remarked that this range error is 
very similar to the range correction which must be 
made in determining the time to fire on a moving 
target. It has been proposed to utilize this similarity 
so that the indicated range of FM sonar can be used 
without this correction in fire-control problems. For 
this application, it is essential that the frequency 
increase, rather than decrease, during each sawtooth 
period. 

Recent development of the gear gives promise of 
utilizing the doppler effect for the determination of 
the range rate, and of eliminating the range error. 

114.4 Comparison of FM and CR Sonars 

Since FM and CR sonars have very similar func- 
tions and both result in plan position indication, it 
is desirable to make a detailed comparison of the two. 
For this purpose the points listed in Section 11.3.2 
will be considered, and in the same order as was 
done there. 


1. The use of doppler to determine the velocity 
of the target is difficult with both systems but may 
be more feasible in the case of FM sonar. The range 
error of FM sonar must be minimized by proper 
choice of its parameters, unless it can be utilized as 
suggested. 

2. In practice, it is found advantageous to listen 
to the echo with FM sonar as well as to watch its 
position on the plan position indicator. It is possible 
that this is also the case with CR sonar. 

3. CR sonar must use a high rate of rotation and 
a wide-band receiver. FM sonar must use a low rate 
of rotation and a narrow-band receiver. Thus FM 
sonar will be less affected by background noise than 
is CR sonar. On the other hand, the slow rate of 
rotation may be a disadvantage for FM sonar in 
certain applications. 

4. The level of reverberation will in both cases be 
determined by the quantity r 0 . This is the radial 
extent of the active area in each case, and can 
be made the same by suitable choice of para- 
meters. 

5. The duration of the echo and the coherence of 
the reverberation will in both cases be determined 
by the rate of rotation. Since FM sonar can be ro- 
tated slowly, its echo duration can be made longer 
than that of CR sonar. This is an advantage of FM 
sonar since the ear can detect and interpret long 
echoes more efficiently than short ones. 

Both systems differ from the standard sonars in 
that the intensity of reverberation is determined by 
other parameters than those that determine the echo 
duration. It does not appear possible to use this ad- 
vantageously in the case of CR sonar. The cor- 
responding problem in the case of FM sonar deserves 
attention. 

6. The target strength is, in both cases, determined 
by r 0 . Both systems have been unexpectedly suc- 
cessful in detecting weak echoes from small targets. 
It may be that this is related to the use of a plan 
position indicator. 

The bearing accuracy achievable by either system 
is determined by the hydrophone directivity. In both 
cases, an increased directivity results in a shorter 
echo. This is less serious with the long echoes of FM 
sonar than with the short echoes of CR sonar. 

In principle, both systems can be adapted to sector 
scanning as well as to the complete 360-degree rota- 
tion. A number of technical problems are different 
in the two cases, but have not yet been fully 
explored. 


THE DETECTION OF SMALL OBJECTS 


219 


The maximum ranges achievable by the two systems 
can be estimated from the foregoing principles. It 
appears that noise is apt to be the limiting factor 
with CR sonar, while reverberation is apt to limit 
the maximum range of FM sonar. There have not 
yet been sufficient experimental measurements, nor 
enough development work, to determine whether 
either system has an ultimate advantage over the 
other. 


THE DETECTION OF 
SMALL OBJECTS 


11.5.1 General Principles 

The echo-ranging gear in use at the beginning of 
World War II was designed for the detection of 
relatively large submarines. As the war progressed it 
became imperative to design equipment for the de- 
tection of mines and other small objects. The stand- 
ard test object in this development work was a sphere 
3 ft in diameter. Its target strength is some 20 db 
lower than that of a large submarine. Because of the 
small target strength, the ranges in small-object 
detection will generally be comparatively short, and 
thus limited by reverberation rather than back- 
ground noise. 

In order than an echo be detected against a 
background of reverberation, it is necessary that the 
total target strength of all the scatterers in the 
active region of a ping should be less than the target 
strength of the sphere; otherwise the reverberation 
intensity will be greater than that of the echo, and 
masking will prevent detection. 

The target strength of the reverberation can be 
decreased by reducing the size of the active region. 
There are two ways in which this can be accom- 
plished: (1) the ping length can be decreased, and 
(2) the beam can be made narrower. The latter 
method is not suitable for shipboard installations 
since it involves a decrease in the effective search 
area and thus would cause great difficulties in main- 
taining contact with the target. That leaves only 
the ping length as an available parameter for this 
purpose. 

The use of short pings is thus a characteristic of 
many sonars designed for small-object detection. The 
reasons for the success, in this phase of echo ranging, 
of CR and FM scanning sonars, which do not use 


short pings, are not clearly understood; as was sug- 
gested above, their success probably depends on the 
plan position presentation of the echo. The present 
discussion will be concerned largely with the use of 
short pings. 

11.5.2 Echo: Reverberation Ratio as 
Function of Ping Length 

The theories developed in the previous chapters 
indicate that the reverberation intensity should be 
proportional to the ping length r 0 ; the echo level, on 
the contrary, should be independent of ping length. 
The latter statement is subject to modification when 
the ping length becomes less than the extent of the 
target in range. If the target is a complicated one, 
its target strength will be less for short pings, as has 
been explained (Chapter 8). This is because the 
echoes from some parts of the target will no longer 
overlap those from other parts. However, if the 
target has a smooth surface, with no irregularities of 
dimensions comparable to one wavelength of the 
sound, this reduction in target strength will prob- 
ably not occur. The theory of echo formation has 
not been worked out with sufficient completeness to 
cover this point. 

The results of some experiments are summarized 
in Table 2. 9 Although they were not suitable for the 


Table 2. Echo ranging on a 3-ft sphere. 


r 0 = ping 
length 

(yd) 

Range 

(yd) 

Echo: 

reverberation 

(db) 

Reverberation 
(db, arbitrary 
reference level) 

To 

10 log 

0.13 

0.13 

82 

23 

26 

0 


290 

19 

9 



360 

11 

15 


0.8 

315 

15 

21 

8 


370 

7 

25 


2.4 

85 

15 

35 

13 


300 

5 

27 



380 

4 

30 


8.0 

85 

14 

46 

18 


300 

5 

27 



calculation of the target strength of a smooth 3-ft 
sphere, they show that the echo-reverberation ratio 
increases with decreasing ping length even when the 
latter is as small as one-eighth the diameter of the 
sphere. They also show that this ratio decreases with 




220 


MISCELLANEOUS ECHO-RANGING APPLICATIONS 


increasing range out to 400 yd, thus supporting the 
idea that reverberation, rather than background 
noise, is the limiting factor in this work. This is rather 
surprising, since a wide-band receiver is necessary 
for the use of these very short pings. The qualitative 
distinction between reverberation and noise largely 
disappears at these ping lengths, for the two sound 
alike to a listener and have a similar appearance on 
an oscillogram. Consequently, these experiments are 
the best evidence that reverberation and not noise 
is the masking agent. This high level of reverberation 
is due to a combination of factors, principally the 
shallowness of the water and the shortness of the 
range. Both are typical of the conditions under which 
the gear must operate. 

In the right-hand column the ratios of the ping 
lengths to the shortest ping length is given. Com- 
parison with the adjacent column shows that the 
reverberation intensity actually is roughly propor- 
tional to the ping length, as predicted by the 
theory. 

11 6 VARIATION OF GAIN 

In Chapter 9, it has been shown that the optimal 
gain setting is one which makes the masking back- 
ground just audible. If the gain is less than this, 
weak signals will not be heard, even though they are 
stronger than the background. If the gain is much 
greater than this, there is danger that a signal will 
overload the amplifier, resulting in distortion and a 
reduction of the signal-background ratio in the 
airborne output. 

This situation is complicated when reverberation 
is the masking background, because the reverbera- 
tion level varies greatly during the period following 
transmission. Many of the oscillograms reproduced 
in this volume show overloading during the early 
period, indicating that the gain setting was too high 
for this period (see Figures 9 and 20 of Chapter 5). 
During a later period, the reverberation is not read- 
able, indicating that the gain setting was too low. 
Other figures show abrupt changes in gain at various 
times, these changes being made automatically to 
avoid these difficulties. 

The obvious solution for this problem is to devise 
a sonar receiver in which the gain continuously in- 
creases during the period following transmission of 
the ping. The receiving circuits for accomplishing 


this time variation of gain [TVG] are controlled by 
the discharge of a condenser that was charged during 
the transmission. By altering the resistance of the 
discharge circuit, the rate at which the gain increases 
can be controlled. By altering the voltage to which 
the condenser is charged, the total increase in gain 
can be adjusted. 10 

While TVG improves the operation of echo- 
ranging gear, it fails to meet all requirements. One 
disadvantage is that the gain is increased in a regular 
manner; this would be satisfactory if reverberation 
decreased in an equally regular manner, but, as has 
been seen, this is not always the case, especially in 
shallow water. Consequently, the possibility of using 
the background to control the instantaneous gain 
was explored. 

Circuits, called automatic volume controls [A VC], 
that could accomplish this had been used in radio 
receivers. The inclusion of these devices in sonar 
receivers proved to be very disadvantageous. The 
A VC circuits can be adjusted so that they respond 
rapidly or slowly to changes in the input. It was 
found that, # if they respond to the rapid fluctuation 
of reverberation, they also respond to the change in 
intensity due to the echo. This is unavoidable, since 
the duration of the reverberation blobs is about the 
same as that of the echo from a point target. With 
this adjustment, A VC reduces the gain during the 
time the echo is being received, an obviously un- 
desirable situation. If, on the other hand, the A VC 
is adjusted so that it does not reduce the gain during 
the echo, it becomes so sluggish that it fails to re- 
spond to the slower changes in mean reverberation 
level, e.g., to the peak of bottom reverberation. 11 - 12 

A compromise solution, called reverberation con- 
trolled gain [RCG], has been developed. This is 
similar to TVG in that the gain constantly increases 
during the period following transmission. It is similar 
to A VC in that the momentary level of the receiver 
input controls its operation. However, it is the rate 
of increase of gain that is controlled and not the gain 
itself. It is obvious that such a device cannot reduce 
the gain when the echo arrives ; it will merely reduce 
the amount by which the gain increases during the 
echo. It will thus not have the disadvantage of A VC. 
It will respond somewhat to the special character- 
istics of reverberation at a specific time and place, 
and thus not suffer the disadvantage of a TVG 
circuit that is improperly adjusted for the momentary 
conditions. 


DEPTH DETERMINATION 


221 


DEPTH DETERMINATION 


11.7.1 Tilting Beam Mountings for 
Transducers 

In Chapter 1 it has been noted that a horizontal 
directional beam may pass over a deeply submerged 
target at close range. As a result, the intensity of the 
sound incident on the target, and consequently that 
of the echo also, are reduced. This renders it difficult 
or impossible to maintain contact at close ranges, 
and the difficulty is increased because of the high 
level of reverberation at short ranges, requiring an 
increased echo level for recognition. 

This can be overcome by mounting the transducer 
after the fashion of a searchlight, so that it can not 
only be rotated about a vertical axis but also tilted 
about a horizontal axis. By depressing the axis of 
the beam toward the deep target, and hence away 
from the surface, the echo level can be increased, and 
the surface reverberation decreased. While such a 
mounting is complicated, both from the standpoint of 
construction and operation, its advantages are great. 


n.7.2 Depth Determination with 
Tilting Beams 


In addition to making it possible to maintain 
contact at short ranges and great depth, the tilting 
beam makes it possible to determine both depth and 
horizontal range. The geometry of the situation is 
shown in Figure 22. The range indicator of the sonar 
shows the slant range R ; the depth of the target below 
the projector is F, and its horizontal range is X. 
Knowing the angle of tilt 0, the values of X and Y 
can be calculated from the equations 


X = R cos 0, 
Y = R sin 0. 


(23) 


Various automatic or semiautomatic methods of 
performing this calculation have been devised. 



Figure 23. Effect of downward refraction on the sit- 
uation shown in Figure 22. The values of the depth and 
horizontal range calculated as above would yield Fo 
and X 0 instead of the actual values Y and X. 

n.7.3 Refraction Error in Depth 
Determination 

Equation (23) assumes that sound rays are straight 
lines. If the rays are refracted, the values computed 
from this equation (call them X 0 and F 0 ) will not be 
the true values, as is shown in Figure 23. The errors 
Y—Y o and X — X 0 can be quite large, especially 
when there is marked downward refraction. 

The errors arise from two causes: the sound does 
not travel in a constant direction, and it does not 
travel at a constant speed. The determination of the 
corrections to be applied is similar to a problem in 
exterior ballistics. The problem can be solved by the 
same methods, but when there is a marked thermo- 
cline, the magnitude of the correction required, and 
consequently the required accuracy of the approx- 
imate calculation, is increased. 

It has been possible to reduce these calculations 
to a semiautomatic form. Several characteristics of 
the bathythermogram are noted, and are used to 
enter a table. This table indicates a single number, 
which designates the proper scale to be used on the 
sonar indicator. These scales are too numerous to be 
engraved on a single plate, so that interchange- 
able plates must be provided. Once the proper 
plate is in position, the correction is applied 
automatically. 




PART III 


LISTENING 




Chapter 12 

THE ACOUSTIC OUTPUT OF SHIPS AND SUBMARINES 


12.1 INTRODUCTION 

12.1.1 Listening to Underwater Sounds 

in Warfare 

T he offensive function of all applications of 
underwater acoustics in warfare is the detection 
and location of enemy craft; the defensive avoidance 
of detection on the part of the patrolling vessel is an 
important corollary. The role of echo ranging in 
subsurface warfare has been described in Part II of 
this book; Part III is devoted to the problems pre- 
sented by listening. A brief comparison of the two 
operations can serve to introduce the subject. 

Echo ranging and listening differ essentially in 
several ways. In echo ranging, the searching vessel 
projects a sound signal into the water intentionally 
in the expectation that the sound will strike a target 
and that enough of the energy will be returned by 
the target to the transducer to activate the receiver 
so that the operator can recognize the echo. The 
primary source of the sound is in the searching vessel ; 
the target is only a secondary source. The transmis- 
sion of the sound is a two-way process. In listening, 
the signal is sound emitted involuntarily by the 
target itself, which therefore is the primary source. 
The transmission is a one-way process. This first 
consideration suggests that losses by transmission 
will be smaller in the case of listening, and that de- 
tection should be possible at longer ranges by listen- 
ing than by echo ranging, provided only that the 
sound output of the targets is comparable to that of 
the standard echo-ranging projector. This last is not 
often the case. a The noisiest type of ship, a large 
battleship moving at high speed, has an overall out- 
put of sound of about the same level as a standard 
projector; but whereas the sound from a projector is 
a pure tone, and the echo has frequencies that are 
restricted to about 100 c in the neighborhood of the 
transmitted frequencies, the sound from a battleship 
has components of a wide range of frequencies, and 
hence is more easily masked by background noise. 
Nevertheless, conditions are frequently such that 

a An obvious and important exception occurs when the 
target is pinging. The enemy can hear the pings at much 
longer ranges than those at which echoes can be detected. 


ships are detected by listening at ranges of 10,000 yd 
and more, whereas echo ranging is rarely effective 
above 3,000 yd. Echo ranging, however, enables the 
range and bearing of the target to be determined 
accurately; listening gives the bearing quite ac- 
curately, but in its most elementary form it provides 
little or no information on the range. 

Listening is used chiefly by submarines. A surface 
vessel produces considerable noise, and this noise 
interferes with the detection of the sounds of other 
ships. This is especially true of the low sounds of 
submarines. On the other hand, this difference in the 
noise output enables a submarine to detect the 
presence of a surface vessel rather easily. An anti- 
submarine surface vessel, moreover, will generally 
not use evasive tactics. Therefore it will not hesitate 
to emit a powerful signal into the water, and thus 
gain the advantages of echo ranging; whereas a sub- 
marine will hesitate to reveal its presence by echo 
ranging except in the last stages of an attack. 

Listening plays an important part in the detection 
of submarines by harbor protection stations. It is 
true that a submarine executing a sneak attack is 
nearly noiseless; still it is not possible to suppress 
all noise, and so a listening watch may provide sev- 
eral minutes of warning. The expendable radio sono 
buoy, dropped from aircraft, carries a hydrophone 
and radios the received sound back to the aircraft. 
Anchored radio sono buoys are used in harbor de- 
fense installations, as are cable-connected hydro- 
phones mounted on the ocean bottom. 

In order that listening be a tactical aid, the sound 
operator must be able : 

1. To distinguish the sound emitted by the target 
from the usual background noise. This requires 
familiarity with both. 

2. To distinguish between the various kinds of 
ship sounds with a view to possible identification of 
the type of vessel emitting them and to obtain 
information on its operating conditions. 

3 . Having detected and perhaps partially identified 
a target, to obtain information concerning its ap- 
proximate location and motion while it is still at 
comparatively long range. 

These considerations suggest the value and pur- 
pose of the investigation of ship and submarine 


223 


224 


THE ACOUSTIC OUTPUT OF SHIPS AND SUBMARINES 


sounds. Other applications of such information im- 
mediately present themselves, besides those just dis- 
cussed. One application is to the problem of the 
control or possible elimination of revealing noises. 
The basic principle in this problem is the same as 
that underlying visual camouflage: to render the 
target inconspicuous by making it resemble its back- 
ground. This means that the sounds that are un- 
intentionally and unavoidably emitted should, in 
the ideal case, have spectra that are very similar to 
that of the background noise. This study, however, 
is still in its beginning stages. 

Another application is found in the design and 
operation of acoustic mines and in the prediction of 
their actuating ranges. This, as well as the defense 
against mines of this type, evidently requires a 
knowledge of the sounds emitted by the vessels 
against which they are to be used. 

12 . 1.2 Basic Factors in Listening 

The physical factors involved in listening are the 
same as those in echo ranging. The target acts as a 
source of sound that must be transmitted to the 
receiver through the water and detected against a 
background of masking noise. The ability of the ear 
or automatic mechanism to recognize the signal 
depends on certain basic factors. 

1. The nature of the signal radiated by the source. 
This will form the subject matter of this chapter. 

2. The transmission loss of sound in water. This 
has been discussed in Part I and will enter only in- 
cidentally into the discussion here. 

3. The nature of the masking sounds. This forms 
the material of Chapter 13. 

4. The response and directivity of the listening 
gear. This is discussed in Section 12.3. 

5. The recognition differential. This is taken up in 
Chapter 14, which deals with psychoacoustic effects. 

The remaining part of this section will discuss the 
nature and method of measuring underwater sounds 
in general; following this, the listening gear in current 
use is described in Section 12.3, and the characteristics 
of the various target sounds are discussed in detail 
in the succeeding sections of this chapter. 

12 . 1.3 Underwater Sound in General 

Underwater sounds are of many diverse kinds. 
The simplest way to distinguish among them is to 


classify them functionally as wanted and unwanted 
sounds. Wanted sounds come from a localized source. 
They can be conveniently designated by their source, 
as ship sounds, submarine sounds, torpedo sounds, 
and the like, or generically by the term “signal.” 
Unwanted sounds come from many possible sources 
and tend to make the detection of the wanted sounds 
more difficult. They are the background noises that 
were decribed in Chapter 9 and include self-noise 
and ambient noise. A more detailed description of 
the spectra of these sounds will be presented in 
Chapter 13. 

Underwater sounds are usually complex; that is, 
they comprise components that have frequencies 
which may range from a few cycles to many kilo- 
cycles per second. The overall intensity of the com- 
posite sound from a given source, as well as the 
manner in which the sound energy is distributed 
among the different frequencies, may fluctuate greatly 
from moment to moment. Hence the complete de- 
scription of an underwater sound will concern itself 
with the spectrum , which shows how the sound energy 
is distributed among the several frequencies, and 
also with the time pattern, which describes the audible 
fluctuation of the sound. Other audible character- 
istics are usually not given a quantitative description, 
and are called the quality of the sound. 

Two general forms of listening gear are used: sonic 
and supersonic. The former consists essentially of a 
hydrophone connected to a loudspeaker through a 
simple amplifier. The latter is similar, but a hetero- 
dyne stage is included, to convert the supersonic 
vibrations into audible sound. 


12 2 THE MEASUREMENT OF 

UNDERWATER SOUND 

12 . 2.1 Response Curves 

Underwater sounds are measured by means of a 
hydrophone connected through an amplifier to some 
form of electrical meter. The latter may be of the 
recording type, or a simple milliammeter. Two kinds 
of recording instruments are used, oscillographs and 
power-level meters. Oscillographs respond rapidly, 
and their record is a more or less faithful graph of the 
instantaneous pressure of the sound on the hydro- 
phone. Power-level meters respond less rapidly, and 
are designed to record the logarithm of the average 


THE MEASUREMENT OF UNDERWATER SOUND 


225 


FREQUENCY, KC 



which are 3 db below the maximum. Another useful 
quantity is the resonance parameter Q =f/w. If Q is 
greater than 10 or 20, the system is said to be highly 
resonant. If Q is less than 4 or 5, the system is 
nonresonant. 

The various components (hydrophone, amplifier, 
loudspeaker) are all characterized by response curves. 
Examples of response curves for some, hydrophones 
are given in Section 12.3. 


FREQUENCY, KC 



Figure 1. Two extreme types of response curves. The 
upper curve is that of a “flat” system which responds 
about equally to sound of any frequency between 
0.1 and 5.0 kc, whereas the lower curve is that of a 
“resonant” system which responds only to sounds in 
the neighborhood of 500 c. 

intensity, i.e., the sound level as defined in Section 1.2. 

All measuring systems must be calibrated. In 
principle, this is accomplished by placing the hydro- 
phone in a sound field of known frequency and level 
and noting the reading. The graph showing the 
reading corresponding to 1 dyne per sq cm at each 
frequency is called the response curve of the system, 
and has already been discussed in connection with 
echo-ranging gear. For the reader’s convenience, the 
discussion is summarized here. 

Response curves of two extreme types are shown 
in Figure 1 . The upper curve is that of a flat system 
which responds about equally to sound of any fre- 
quency between 0.1 and 5.0 kc, while the lower curve 
is that of a resonant system which responds only to 
sounds in the neighborhood of 500 c. Both kinds of 
system have their uses. A flat system can be converted 
into a resonant system by the insertion of a filter. 

Systems whose response curves have a maximum 
at a frequency / are said to resonate at that fre- 
quency. The width w of the resonance peak (see 
lower curve, Figure 1) is usually defined as the 
frequency separation of the two points on the curve 


12 . 2.2 Overall Levels 

Most sounds encountered in listening are not pure 
tones of a definite frequency or pitch. When a com- 
posite sound is measured with two systems having 
different response curves, the two meter readings 
will usually be different. In order to obtain compar- 
able results, some correction must be made. 

This correction is simple only in the case of flat 
systems, where response is practically independent 
of frequency. In that case, the meter reading minus 
the numerical value of the response (10 db in the 
system represented by the upper curve of Figure 1) 
is a number which is independent of the system. It 
is called the overall level of the sound. 

Ideally, the overall level should be measured with 
a system in which the response curve is a horizontal 
line extending from 0 c to infinity. Practically, such 
systems are impossible to build, and a compromise 
is necessary. In the present book, the overall level is 
supposed to be measured with a system that responds 
equally to all frequencies between 0.1 and 10 kc, but 
with a response curve which drops rapidly outside 
this range. 

The overall level is a useful characteristic of a 
sound, but does not completely describe it. There are 
circumstances in which one sound of given overall 
level may be audible, while another of the same 
overall level is inaudible. 

12.2.3 Spectrum Level 

In order to discuss those properties of sounds that 
are not determined by their overall level, it is con- 
venient to use the concept of spectrum level, which 
was defined in Chapter 9. 

The spectrum level is defined in terms of an ideal 
system, but can also be determined from the reading 
of an actual system, provided its response is suf- 




226 


THE ACOUSTIC OUTPUT OF SHIPS AND SUBMARINES 


ficiently peaked. The effective bandwidth w of an 
actual system must be determined in a way that need 
not be discussed here. Often the definition of w as 
the width of the resonance peak between the 3-db 
points can be used. Spectrum-level meters are of two 
kinds, one of which is furnished with a series of filters 
of known width and mid-frequency. The other kind 
is arranged so that the mid-frequency of its response 
is continuously variable, the bandwidth remaining 
constant. 

For any sound, the spectrum level can be plotted 
as a function of the frequency (see Figure 15). Such 
a graph is called the spectrum of the sound. 

It sometimes happens that more or less pure tones 
are emitted simultaneously with a sound having a 
continuous spectrum. This occurs, for example, when 
a propeller is driven through a gear train that has 
not been quieted, or when the propeller blade vi- 
brates like a whistle because of the flow of water 
past its blades. Such single-frequency sounds can be 
shown on the spectrum as very high, narrow peaks. 
The accurate measurement of these peaks presents 
practical problems that need not be considered here. 

For convenience, these peaks are called “lines.” A 
spectrum that does not contain lines is a continuous 
one. A line spectrum may be superposed on a con- 
tinuous one (see Figures 23 and 24) or may occur 
without any noteworthy continuous spectrum (as 
in the case of a musical instrument). 


12.2.4 Oscillograms 

A sound is not determined uniquely even by its 
spectrum. For many purposes, however, two sounds 
having the same spectrum may be considered as 
equivalent, even though they may be recognizably 
different to the ear. Descriptive terms, such as 
“hissing,” “burbling,” “crackling,” are often useful 
in this connection. 

If more detailed information about the sound is 
needed, an oscillogram recorded with a flat system is 
obtained. This is essentially a graph of the instan- 
taneous pressure in the sound wave as a function 
of time. 


12.2.5 Distortion 

If a sound is passed through a system whose 
response is not flat, it will be distorted. That is, if 


FREQUENCY, KC 

a i i.o io ioo 



So 


SYSTEM 

R (f) 


S(f) 


Figure 2. Diagram illustrating the effect of the re- 
sponse of a system on the spectrum of an incident 
sound. If S(f ) is the spectrum of the incident sound 
and R(f ) the response of the system, the output will 
have the spectrum S 0 (J) =S(f) +R(f). 


the output stage of the system is a loudspeaker, the 
sound emitted will not be a faithful reproduction of 
the incident sound. If the output of the system is a 
voltage, the changes in this voltage will not be pro- 
portional to the changes in the sound pressure. 

If S(f) is the spectrum of the incident sound and 
R(f ) the response of the system, the output will have 
the spectrum S 0 {f ) =$(/) + #(/). This is illustrated 
by Figure 2. 


12.2.6 Inherent Threshold 

Most measuring systems are arranged so that their 
sensitivity can be varied in steps, resulting in a shift 
of the response curve parallel to itself by a known 
number of decibels. For sounds of high level, a low 
sensitivity is sufficient; for sounds of low level, 
high sensitivity is needed. 

As the sensitivity is increased, a stage will ulti- 
mately be reached when the meter shows a reading 
even though the hydrophone is in a very quiet place. 
This is caused by electrical and other noise originat- 
ing in the measuring system itself. The inherent 
threshold has already been discussed in Chapter 9, 
and is the sound level which would, in the absence 




HYDROPHONES 


227 


of the system noise, cause the same meter reading 
as the system noise. 

Sounds which are much below the inherent thresh- 
old cannot be measured. Sounds at the threshold 
level can be detected by a change in the meter read- 
ing (theoretically, 3 db) but a correction must be 
applied to the reading in order to obtain the true 
sound level. Not until the incident sound is 6 or 10 
db above the threshold level can the meter reading 
be used without correction. 

This concept of threshold is an important one, 
and can also be applied to the components of a 
system, as well as to the ear itself. 

123 HYDROPHONES 


12 3 .i The Response of Hydrophones 

When a hydrophone is placed in an underwater 
sound field its diaphragm oscillates in response to the 
variations in hydrostatic pressure at its face. These 
oscillations of the diaphragm are transformed into 
electric energy as discussed in Sections 7.2 and 7.3. 

The magnitude of the voltage generated in the 
receiver is a function of the pressure on the diaphragm 
of the hydrophone. This response of the hydrophone 
partially determines the response of any system into 
which the hydrophone may be connected. Hydro- 
phone response at the frequency / is defined as the 
electromotive force developed in the hydrophone 
when it is in a sound field of frequency / and rms 
pressure of 1 dyne per sq cm. 

If e is the emf generated by the hydrophone when 
in a sound field of p dynes per sq cm, its response is 


FREQUENCY, KC 

10 20 30 40 50 



Figure 3. Response curve of a standard supersonic 
hydrophone. 10 


20 log (e/p) db. It will, in general, be a function of the 
frequency, as discussed above. Very few hydrophones 
have flat response curves; exceptions are a few 



Figure 4. Response curves of a standard sonic hydro- 
phone, used with and without a baffle. 10 


specially designed for scientific measurements. In 
Table 1, typical values of the response of various 
hydrophones are given in Column 7. Figures 3 and 4 
show detailed curves for standard sonic and super- 
sonic hydrophones. 


Table 1 . Characteristics of some commonly used hydrophones. 10 


Code 

Type 

Approximate 
diaphragm 
diam (in.) 

Resonant 

frequency 

(kc) 

Directivity 

index 

(db) 

Resonance 

parameter 

(Q) 

Hydrophone 
response (db 
above 1 v per 
dyne per sq cm) 

Threshold 
(db above 

1 dyne per sq cm) 

QC 

MS* 

15^ 

24 

-22 

10 to 110 

- 80 to - 85 
(24 kc) 

-92 

QBG 

RS* 

8H 

Broad 

-17 

3 to 6 

- 80 (24 kc) 

-98 

JK 

RS 

15h 

Broad 

-23 

3 

- 64 (24 kc) 

-105 

British ASDIC 

Quartz 

15 

15 

-22 

55 to 80 

— 42f(15 kc) 

-107 

JP 

MS 

2x40 

(tube) 

Broad 

0 (0.1 kc) 
-8.0 (5.0 kc) 
-11.0 (10 kc) 


- 135 to - 105 
(0.1 to 10 kc) 

-48 to -67 


* MS Magnetostriction unit; RS Rochelle salt unit. 

t This is not the emf but the measured response in the actual operating gear. 


228 


THE ACOUSTIC OUTPUT OF SHIPS AND SUBMARINES 


120 ° 90 ° 60 ° 



Figure 5. Directivity patterns of the sonic hydrophone 
whose response curves are shown in Figure 4. 10 


i2.3 2 The Directivity of Hydrophones 

The response of large hydrophones depends on the 
direction from which the sound is incident (see 
Section 7.4). In interpreting response curves, it may 
be taken for granted that they refer to the direction 
of maximum response, unless specifically stated 
otherwise. The direction of maximum response 
is usually called the axis of the hydrophone, 
although other definitions of this term are used 
occasionally. 

In the following comparisons of a directional and 
a nondirectional hydrophone, it is assumed that the 
latter has the same response curve for all directions 
as the former has for its axis. 

Directional hydrophones are usually mounted so 
that they can be rotated about a vertical axis. The 
bearing of a target can thus be determined by noting 
the direction in which its sound is a maximum. Since 
a change of 3 db in sound level is usually quite per- 
ceptible, reasonably accurate bearings can be ob- 
tained even with hydrophones with patterns similar 
to those of Figures 5 or 6. 

While the possibility of obtaining bearings is the 
primary reason for installing directional hydrophones, 
they have several other advantages over nondirec- 
tional systems. These all arise from the necessity of 
distinguishing between the signal and the back- 
ground of unwanted sound. 

If the source of the background noise is localized 
(e.g., at the propellers of the listening ship) on some 
bearing other than that of the target, the directional 
hydrophone will suppress the unwanted sound rela- 
tive to that of the target. Thus listening may become 


120 ° 90 ° 60 ° 30 ° 



Figure 6. Directivity patterns of a standard hydro- 
phone for frequencies of 20, 26, and 30 kc. 10 

possible with a directional system even though the 
background is too high for the use of a nondirectional 
system. 

This is true even of the background of ambient 
noise, for which the sources are distributed in all 
directions. The directional hydrophone will respond 
mainly to those sources that lie on its axis. Thus its 



HYDROPHONES 


229 



response to ambient noise will be less than that of a 
nondirectional one. Its response to a target located 
on its axis will, however, be the same as that of the 
nondirectional hydrophone. The difference in the 
background heard by a given nondirectional hydro- 
phone and that heard by the directional unit is 
called the directivity index of the latter (see Section 
7.4). Column 5 of Table 1 gives typical values of the 
directivity indices. 

Finally, the listener can control the level of the 
signal from a localized target by training a direc- 
tional hydrophone on and off. Since the background 
of ambient noise remains constant during such a 
sweep, this procedure is an aid in verifying a sound 
contact. 

12.3.3 Sonic Listening Gear 

These general remarks can be illustrated by 
considering the directivity pattern of a particular 
hydrophone. The JP hydrophone is a cylindrical 
nickel tube about 3 ft long and 2 in. in diameter which 
serves as a magnetostriction unit. It is mounted, 
with the tube horizontal, on a vertical shaft about 


which it can be rotated, as indicated in the illustra- 
tion of Figure 7. The directional properties are de- 
termined by the ratio of the tube length to the 
wavelength of the incident sound. When sound pres- 
sure reaches all parts of the tube simultaneously, as 
it does when the tube is at right angles to the direction 
of the impinging wave, the generated voltage will be 
at a maximum. When the tube is turned to intercept 
the wave obliquely, the pressure on a given area will 
be greater or less than the pressure on an adjacent 
area. As a consequence, if the wavelength is small, as 
it is at the higher frequencies, some parts of the tube 
will be caused to expand while other parts will be 
compressed. These opposing effects on different parts 
of the tube tend to reduce the response of the hydro- 
phone. If the wavelength is long compared to the 
length of the tube, all parts of the tube will be com- 
pressed or expanded in nearly the same phase, hence 
the orientation of the tube will have little effect on 
the response; in other words, the hydrophone will 
be practically nondirectional. Thus, the hydrophone 
becomes more directional as frequency increases and 
wavelength decreases. 

Figure 5 is a directivity pattern of the JP unit for 
sound of a frequency of 4.7 kc. The patterns were 
taken in a plane containing the axis of the cylinder. 
They show two main response peaks or lobes and 
numerous side lobes. The JP is usually provided with 
a sound-absorbing baffle, and it is seen by comparing 
the two patterns that the baffle causes a drop of 10 
db in the rearward direction; this additional direc- 
tivity aids in discriminating against the self-noise due 
to the propellers, and also helps to prevent errors of 
180 degrees in target bearings. At the frequency of 
about 5 kc, the main lobes are seen to be about 
20 degrees wide (between the — 3-db points) ; at 
higher frequencies they become narrower and 
the hydrophone correspondingly more directional. 
In a plane perpendicular to the axis of the 
tube, the JP hydrophone without baffle is non- 
directional. 

The JP amplifier has five filters of the high-pass 
type. The cutoffs are at 0.2, 0.6, 1.5, 3.0, and 5.5 kc. 
The operator, using headphones, will begin by listen- 
ing with the lowest filter frequency switched on, for 
many of the wanted incidental sounds have very 
strong components at low frequencies. On identify- 
ing a signal, he will successively switch on the higher 
frequency filters in order to utilize the progressively 
increasing directivity of the unit. There is a “tuning 


230 


THE ACOUSTIC OUTPUT OF SHIPS AND SUBMARINES 


eye” permanently connected to the output of the 
5.5-kc filter, which facilitates the determination of 
the bearing. A skilled operator may expect to obtain 
bearings that are accurate to within 1 degree with 
the JP gear. 1 

12.3.4 Supersonic Listening Gear 

Supersonic listening has certain advantages asso- 
ciated with the greater directivity and sharper response 
at the higher frequencies. The JK hydrophone illus- 
trates this. It is a Rochelle salt crystal unit, with a 
circular diaphragm, and is mounted in a spherical 
housing to reduce the water noise. On surface vessels, 
the sphere may itself be enclosed in a streamlined 
dome. Directivity patterns shown in Figure 6 illus- 
trate the increase in directivity as the frequency 
increases. Figure 3 shows the response curve of this 
unit for sound incident along the axis. It is seen that 
there is a broad peak at 24 kc. The response drops 
3 db below the maximum at 24 kc in the frequency 
band from 21.5 to 27.5 kc. The value of the resonance 
parameter Q is thus 24/6 or 4. In contrast to this 
broad response band with the low value of Q is the 
very narrow response band of echo-ranging trans- 
ducers like the QC, which at a resonant frequency of 
24 kc have values of Q ranging from 10 to 110. A Q 
of 25 would restrict the listening to a band of a few 
kilocycles centered at 24 kc, if a nonresonant amplifier 
is used. 

The narrower pass band associated with a high- 
resonance parameter is advantageous in echo rang- 
ing, but not in listening. If the incident sound has a 
more or less uniform spectrum level throughout the 
frequency band in question, the output of the listen- 
ing gear is proportional to the pass-band width. Most 
background noise is of this description and its level 
is reduced by narrowing the pass band. This is an 
advantage in echo ranging (see Section 9.1) . In listen- 
ing, however, the signal is also reduced in level, and 
no advantage is gained. The pass band would thus 
appear to be immaterial. However, listening through 
a narrow-band system distorts the sound so that 
everything sounds the same ; the operator thus loses 
the advantage of any qualitative difference between 
signal and background, unless the former has a 
characteristic time pattern. 

The higher directivity of the supersonic hydrophone 
makes it possible to avoid receiving much of the noise 


caused by the motion of the listening vessel. As a 
result of this and other factors, supersonic listening 
is possible at ship speeds of 15 to 20 knots, compared 
with the maximum speed of about 5 knots that limits 
sonic listening. 

12.3.5 Enemy Listening Gear 

The German and Japanese navies have stressed 
sonic listening more than have the United States and 
British. They have tended to use several small hy- 
drophones, mounted some distance apart. The out- 
puts of these are combined in such a way that the 
installation as a whole is directional. By means of 
variable elements in the electric circuits, it is possible 
to alter the direction of maximum sensitivity of such 
hydrophone arrays. The sound beam can thus be 
steered without the necessity of moving parts outside 
the hull. 


12 4 SOUNDS OF SUBMARINES 


12.4.1 Objectives 

From the antisubmarine standpoint, a knowledge 
of the sound output of submarines is needed for the 
prediction of maximum listening ranges. The design 
of listening gear, in particular the decision between 
sonic and supersonic devices, depends on the spectrum 
of the sound to be detected. 

From the pro-submarine standpoint, it is impor- 
tant to know the relative sound output of various 
maneuvers, so that evasive action will not be nulli- 
fied by excessive detectable sound. The problem of 
noise control, and the design of propellers, engines 
and auxiliaries, all demand measurement of sound 
output. 


12 4.2 The Sources of Submarine Sounds 

Submarine sounds have their origin chiefly in the 
machinery and in the propellers. 

The machinery of the submarine is extremely 
diversified and complicated. There are more than 
fifty auxiliaries, all of which are potential sound 


SOUNDS OF SUBMARINES 


231 


OVERALL SOURCE LEVEL, DB 
10 20 30 40 50 


BOW PLANE 
(HAND) 





BOW PLANE 
(POWER) ' 





STEERING 





DRAIN PUMP 





PERISCOPE 





TRIM PUMP 





STERN PLANES 

(hand) 





STERN PLANES 
(POWER) 





STARBOARD ASTERN 
PORT AHEAD 40 RPM 





STARBOARD AHEAD 
PORT ASTERN 40 RPM 






BEST NAVAL MAXIMUM 

PRACTICE ' ' PERMISSIBLE LIMITS 

Figure 8. Suggested limits of overall sound level of 
several auxiliaries on submarines, and the levels rep- 
resenting best naval practice. 

sources. Figure 8 lists a few of these sources, and 
shows the source levels that have been proposed as 
best naval practice and also the maximum permis- 
sible limits. 

In general, these sounds have a continuous spec- 
trum, with a maximum at low frequencies. Sometimes, 
however, the machinery will produce a strong line 
spectrum which is superposed on the continuous 
spectrum. The importance of such single-frequency 
components warrants a rather detailed discussion, 
and this will be found in Chapter 14. 

Propeller sounds are of two general kinds, (1) 
singing , due to vibrations of the propeller blades, and 
(2) cavitation sounds. The latter are the most im- 
portant of all submarine sounds. Vibrations of the 
propeller blades may be due to faulty design 
or manufacture and are generally not difficult to 
eliminate. 

Cavitation results when the propellers are turning 
so rapidly that the water does not close in behind the 
blades. Thus a stream of bubbles is formed. These 
may be caused by reduced pressure on the back of 
the propeller blade (Figure 9) or by vortices at the 
tip of the propeller blade (Figure 10). Acoustically , tip 
cavitation appears to be much more important than 
blade cavitation. This may be because the blade 
cavitation has a more serious effect on propeller 
thrust, and is usually prevented by the designer of 
the ship. These bubbles cause noise in much the same 
way as those in a boiling kettle. 


Besides these two main sources of submarine sounds, 
there are some minor sources, such as the splashing 
of water at the bow and in the wake when the sub- 
marine is at the surface; when submerged, the fittings 
of the vessel, such as handrails, may be set into vi- 
bration by the turbulent flow of water past them. 
These sounds are considered to be of small signifi- 
cance compared with those due to cavitation. 

The activities of the crew are a source of incidental 
sound. It is interesting that, according to some Brit- 
ish measurements, overall source levels of 45 to 50 db 
may be produced by dropping a spanner or by the 
use of the engine-room telegraph, levels comparable 
to those produced by the submarine itself under con- 
ditions of evasive operations. The transitoriness of 
such sounds makes them comparatively unimpor- 
tant, except when evading detection by an alert 
enemy. 

12.4.3 The Measurement of 

Submarine Sounds 

The measurement of source levels involves (1) the 
sound levels, (2) the distance between the hydro- 
phone and the source of the sounds. 

If the measurements are taken in a sound range, 
the hydrophones are moored to the bottom at ac- 
curately determined positions. The submarine carries 
out its maneuvers both on the surface and at peri- 
scope depth. Its position at all times can be accurately 
determined from shore and recorded, and thus the 
range which the signal sound has traversed at any 
given moment can be calculated from simple geom- 
etry. The levels of the sounds received at the hydro- 
phones are also measured ashore, as a function of 
time. This method is at present restricted to relatively 
shallow water. It would be desirable to have a sound 
range at least 400 ft deep, to enable maneuvering at 
greater depths. 

A second method is used when no sound range is 
available or when measurements in deep water are 
desired. The sounds are recorded on a surface vessel 
equipped as a sound laboratory, and dead in the 
water. The hydrophone is streamed out on buoys to 
avoid the effects of the noise originating at or on the 
vessel. The submarine follows a straight course past 
the hydrophone, approaching it as closely as possible. 
Unless the submarine is on the surface or at periscope 
depth, unavoidable inaccuracies enter the range 
measurement. 


232 


THE ACOUSTIC OUTPUT OF SHIPS AND SUBMARINES 


SPEED, KNOTS 



Figure 9. Overall source levels of submarine sounds. 

(A) Submerged variation with speed; (B) two sub- 
marines, surface operation, illustrating the variability 
between ships. 

In such experiments, the received sounds have also 
been sent by frequency-modulated radio to a lab- 
oratory on shore, where high-fidelity sound-on-film 
records are made for later detailed study and meas- 
urement. 

The sounds produced by individual sources may 
also be measured at dock by hanging hydro- 
phones overside and operating various auxiliaries 
successively. 

The sound output may also be monitored by the 
submarine crew while the vessel is on actual opera- 
tions. This can be done with the standard JK and 
JP listening units by making a sweep from 0 to 
360 degrees and noting the readings on a meter. 
However, a special noise-level monitor is prefera- 
ble for such purposes. 2 * 3 This is an installation 
of four small magnetostriction hydrophones placed 
near the noisiest auxiliaries but outside the pressure 
hull; a fifth hydrophone is installed near the 
propellers. The signals from each of these hydro- 
hones can be amplified and measured at will. 


The output of the several hydrophones is recorded 
when the submarine is quiet, and this is compared 
with their respective output when the vessel is 
operating. 

12.4.4 Overall Source Levels of 
Submarine Sounds 

The sound output of a submarine varies widely 
with the size and type of vessel. For a given vessel 
it varies with speed and operating conditions. If the 
submarine is submerged, its sound output depends 
strongly on the depth of submergence. 

The overall source level may range from about 40 
db under evasive conditions to more than 75 db at 
top speeds. 4 An average based on a large number of 
measurements 5 gives the following values. (1) Run- 
ning submerged at 6 knots or at 12 knots on the 
surface, the overall source level is about 72 db. (2) At 
top surface speeds, the overall source level is about 
77 db. 

The dependence of the overall source level on speed 
is shown for two submarines in Figure 9. In diagram 
A the overall source level is plotted against the ship 
speed for a submerged submarine, and in the right- 
hand diagram, for two submarines operating at the 
surface. 

The variability of source level from ship to ship is 
indicated by the curve of vessel B included in dia- 
gram B. The values of source levels of various sub- 
marines may vary by as much as 10 to 15 db under 
identical operating conditions. 

The curve pertaining to operation at periscope 
depth is typical of ship sounds in general. At 
very low speeds the source level is quite low. At a 
certain critical speed, in this case 4 knots, the 
sound output increases very rapidly with speed, so 
that an increase of 2 knots is accompanied by 
an increase in the source level of 30 db. If the 
speed is increased beyond 6 knots, the curve 
flattens off. 

This abrupt increase in the sound output at the 
critical speed is due to cavitation, which is related to 
many factors but chiefly to the shaft rate or speed 
and to the hydrostatic pressure. Other things being 
equal, the speed at which cavitation occurs is in- 
versely proportional to the square root of the static 
pressure. (See Chapter 5.) Hence one would expect 
the sound output at a given speed to be less when 
the submarine submerges to greater depths. This is 


SOUNDS OF SUBMARINES 


233 


v/Vh 




Figure 10. Dependence of overall source levels of sub- 
marine sounds on depth of submergence h (feet) and 
speed F (knots). The steep rise between V/h A =0.4 and 
V/h A = 0.6 is due to cavitation. The solid curve is 
drawn on the assumption that the speed at which cav- 
itation occurs is inversely proportional to the square 
root of the hydrostatic pressure. 5 Figure 10A plots the 
levels measured in the 0.1- to 10-kc bandwidth; Figure 
10B the levels in the 10- to 30-kc band. 

shown to be the case in Figure 10, 5 in which overall 
source levels are plotted against V/h' A , where V is 
the speed in knots and h is the total hydrostatic 
pressure head. The value of h is calculated from 
h = 33 + d, where d is the depth in feet and 33 ft is 
the head of sea water equivalent to 1 atmosphere. 
The experimental points are seen to fit the em- 
pirical curves fairly well. They are based on a small 
number of data obtained from two submarines of 
the same size and design. 

It has been found that the speed required for 
cavitation to set in is, in general, higher for sub- 
marines of new design. This is the result of a per- 
sistent effort to decrease the sound output of American 


FREQUENCY, KC 



Figure 11. Average spectrum of a submarine running 
at 6 k at periscope depth or 12 k at the surface. It must 
be stressed that the spectra of individual ships may 
deviate decidedly from this figure. 5 

submarines. It has been decreased, on the average, 
about 20 db; however, individual submarines occa- 
sionally are still found which produce prominent and 
very undesirable single-frequency tones below 1,000 
c. There is considerable evidence that these have 
their origin almost entirely in the reduction gears. 

The relation between sound level and speed is 
quite different for surface operation. Referring to 
diagram B of Figure 9, it will be noted that the in- 
crease in source level of submarine A is gradual and 
does not show the abrupt rise due to cavitation that 
is observed with submerged operation. The higher 
levels associated with surface operation are to be 
attributed to the diesel engines used for operating on 
the surface; the electric drive is considerably more 
quiet. The hump shown in the curve for submarine 
A is caused by a singing propeller. 

12.4.5 Sound Spectra of 

Submarine Sounds 

Figure 1 1 gives the spectrum of a submarine run- 
ning at 6 knots at periscope depth or at 12 knots on 
the surface. These values are averages based on a 
large number of measurements. It must be borne in 
mind that there is a great spread in individual 
measurements, and thus the sounds from a given 
submarine may deviate decidedly from the values in 
the figure. 5 

It is seen from Figure 11 that the intensity of 
submarine sounds decreases rapidly with the fre- 
quency; the drop in level is about 6 db per octave on 
the average. In other words, the spectrum level is 
about 20 db higher at 100 c than at 1,000, and this 
same proportionate variation continues at least until 




234 


THE ACOUSTIC OUTPUT OF SHIPS AND SUBMARINES 


FREQUENCY, CPS 







DEPTH 

• 55' 
a. 100' 
o 200' 
o 300' 





/} 


M • 


flv 









r 

0 -nil 



=8=8= 

-o 



( 

0 0 0 0 

^ D 


















o" 

B 








Figure 12. Spectra of individual submarines. (A) 
The variation of spectra with speed of submerged sub- 
marine; (B) effect of increasing depth on the spectra. 5 
The peak which characterizes the curves at low fre- 
quencies is ascribed to cavitation. 


30 kc. As a result, the overall level is largely de- 
termined by the lower frequencies. 

If the threshold of listening gear were independent 
of frequency, sounds with such a spectrum would be 
much more readily detected with sonic than with 
supersonic devices. However, the threshold also de- 
creases with increasing frequency, especially for gear 
mounted on a moving surface vessel, and until re- 
cently this has more or less nullified the advantage of 
sonic listening. These problems will be discussed again 
in Chapter 15. On sailing vessels, sonic listening 
retains its advantage, especially if the auxiliaries can 
be periodically shut down for listening. An effective 
antisubmarine watch can thus be maintained from 
such vessels. The same is true of bottom-mounted 
hydrophones and sono buoys, both of which use the 
sonic band. 

Sound-level spectra of individual submarines are 
shown in Figures 12 and 13 for various operating 
conditions. A characteristic feature of these curves 
is a peak at low frequencies, and a tendency for this 
peak to occur at lower frequencies as the speed in- 
creases. This behavior is ascribed to cavitation effects. 


FREQUENCY, CPS 


100 200 500 1000 10000 

60 1 r— 






RPM SPEED KNOTS 
230 o 16.5 

170 o 12.0 

150 A 1 1.0 

110 • 8.0 . 

□ 





0 



°- Q-r^ 

kCT’X 






• 

,A- 

d "8q— . 

D 







kslb; 




0- 
























Figure 13. Variation of spectra of individual subma- 
rines with speed. Surface operation. 


It is thought that higher propeller speeds produce 
progressively larger bubbles. The resonant frequency 
of a bubble is inversely related to its diameter (see 
Chapter 5), and thus an increase in speed results in 
the production of sound of a lower frequency. 

The exact position of these peaks also varies from 
submarine to submarine. Consequently they do not 
show on the average curve of Figure 11. It will be 
noted that even the peaks of these two submarines 
lie well below the average curve for frequencies less 
than 1 kc. 

Figure 12B shows the effect of increasing depth on 
the sound-level spectrum. It will be noted that the 
peaks tend to shift toward higher frequencies with 
increasing depths. It is thought that the increase in 
hydrostatic pressure with depth reduces the size of 
the cavities formed at a given speed, and thus results 
in a higher resonance frequency. 


12.4.6 The Directivity of 

Submarine Sounds 

Very little is known concerning the location of the 
particular point, or points, on the ship which can be 
considered as the effective source of the radiated 
sound. There is reason to believe that at periscope 
depth the engine room is the principal source of 
sounds at very low speeds, while at speeds above 3 
to 4 knots the propeller is chiefly responsible. How- 
ever, even at high speeds the engine room may con- 
tribute materially to the sound at frequencies below 
150 c. During surface operations the propeller and 
wake are probably the principal sources of sound at 
practically all speeds with electric drive; with diesel 
drive the engine room is the main source at low speeds, 
and a material contributor at all speeds. 


SOUNDS OF SURFACE SHIPS 


235 


The sounds from submarines are radiated in such 
a way as to produce approximately a uniform sound 
field at a distance of several ship lengths from the 
source. Some -observers * * * 5 report a slight decrease in 
the sound level in the region within 10 or 20 degrees 
on either bow; at 200 yd it amounts to from 2 to 4 
db. A similar shadow astern of the ship has also 
been reported; this is ascribed to the wake. 

12.5 SOUNDS OF SURFACE SHIPS 

12 . 5.1 Objectives of the Study of 

Ship Sounds 

The sounds emitted by surface vessels may pro- 
vide considerable information to an experienced sound 
operator aboard a submarine. Various forms of under- 
water mines are detonated by the ship’s sound. Ship 
sounds vary greatly from ship to ship, and from one 
class of ship to another, in intensity and spectrum, 
and for a given ship, both vary with speed. From the 
viewpoint of defense, it is obvious that every ship 
that is likely to enter water harboring hostile sub- 
marines, would benefit by an analysis of its own 
sounds. Such an analysis would discover any reveal- 
ing single-frequency components, such as the one 
shown in Figures 23 and 24. These undesirable com- 
ponents are due to causes which can often be easily 
remedied. The analysis would also make possible 
more accurate estimates of the range at which the 
ship is liable to be detected by an enemy submarine 

12.5.2 The Measurement of Ship Sounds 

The following procedure 6 is typical of the methods 
used for measuring the acoustic output of surface 
vessels. A series of hydrophones was mounted on 
tripods on the sea bottom in water 40 ft deep. As a 
ship passed over the hydrophones, the sound output 
was recorded, together with data on the type and 
speed of the vessel, its changing position, etc. In 
tabulating the results, the maximum response from 
the various hydrophones was used. The recorded pres- 
sure levels were reduced to source levels. Both overall 
pressure levels and spectrum levels were recorded. 

12.5.3 The Overall Sound Output of Ships 

The extreme values of observed overall source 
levels range from about 50 db for launches and small 


FREQUENCY, KC 



Figure 14. Spectrum of surface ships, representing 
the average of measurements made of 52 vessels of 
12 different types of warships and commercial ships. 


auxiliary craft at low speeds to 1 10 db for battleships 
at 20 knots. 7 The latter value is approximately the 
source level of a standard sonar projector. It will be 
recalled that the average overall source levels of sub- 
marines ranged from about 30 to 75 db. 

Besides being affected by the speed of the vessel, 
the overall source level is a function also of the load 
or displacement of the ship. b 

12.5.4 Spectra of Ship Sounds 

The sources of ship sounds are extremely diver- 
sified, and a given source may change its sound 
output with ship speed. Hence ship sounds are 
variable and complex, and are distributed through 
the whole range of frequencies. As in the case of 
submarines, the chief sources are the screws, where 
cavitation produces the sound, and the hull, which 
transmits the vibrations of the machinery and engines. 

Single-frequency components due to propeller sing- 
ing or to vibrations of the propulsion machinery are 
common. Ordinarily such sounds occur below 1 kc, 
but sometimes these single-frequency components 

b An empirical formula is given in Survey of Underwater 

Sound, Report No. 4, 7 which has been found fairly accurate 

when applied to ships of over 400 tons’ displacement. It is 

S = 60 log K + 9 log T- 25, 
where S = spectrum level at 5 kc at 1 yd from source, 

K = the speed of the ship in knots, 

T = the displacement in tons. If this is not known, 
the gross tonnage either can be estimated or is 
listed for the type of a given vessel. Even a large 
error in T does not affect the value of S signif- 
icantly. For instance, if a 3,000-ton ship displace- 
ment were estimated as 6,000 tons, the error in S 
would be less than 3 db. 


THE ACOUSTIC OUTPUT OF SHIPS AND SUBMARINES 


236 


CD 

O 

</T 

_i 

u 

> 

UJ 


2 

D 

cr 

H 

O 

UJ 

0. 

V) 


Figure 15. Average spectra of six different classes of ships. 



are encountered well above this frequency. They are 
discussed in some detail in Chapter 14. 

Figure 14 shows the average spectrum-frequency 
distribution of sounds from a large number of surface 
ships. 7 The data on which this figure is based were 
provided by measurements made according to the 
method described above on 52 ships comprising 12 
different types, including both warships and com- 
mercial vessels. The ordinates on the graph are the 
values of relative spectrum levels, i.e., of the spec- 
trum level, defined above, minus the overall (0.1- to 
10-kc) level. These differences are averaged for all 
types of ships in order to obtain the graphs. The 
total spread of the measurements on the individual 
ships was considerable, and due allowance for this 
must be made when using data from this graph and 
the following graphs. 

The level of the sound is seen to decrease with 
increasing frequency, at a rate of 7 db per octave. 
This is very similar to that shown in Figure 11 for 
submarines. Spectra of the different ships varied in 
average slope from about 5.5 to 8.6 db per octave. 
Figure 15 shows average spectrum levels for six 
different classes of ships at normal cruising speeds. 
The average overall levels are also indicated. 


FREQUENCY, KC 



Figure 16. Effect of varying speed on ship spectra. The 
curve marked L represents the average spectrum at 
low speeds, H that at high speeds, and N that at normal 
cruising speeds. 

Figure 16 illustrates the effect of varying speed on 
the spectral distribution. At very low speeds the 
chief source of the sound is found in the machinery, 
and all the machinery contributes materially. Much 
of the sound from this source is concentrated at the 
lower frequencies; therefore in this region the spec- 
trum is highly variable, as was previously noted in 
the case of submarines (Section 12.4). The curve 
marked L indicates the approximate shape of the 


TIME PATTERNS AND PROPELLER BEATS 


237 


135 ° 90 ° 45 ° 



135 ° 90 ° 45 ° 



Figure 17. Contours showing the average directional- 
ity of ship sounds. (A) Average patterns for 15 freighters 
for low frequencies (200-400 c) ; (B) contours of sound 
levels for a typical freighter at 8 k. The outline of the 
ship is indicated by the shaded area. 7 

spectra for low speeds. It is seen to differ markedly 
from the spectrum at normal cruising speeds, which 
is very similar to Figure 14 for frequencies above 
1,000 c, but is also quite variable at lower frequencies. 
The variability of the spectra in the lower frequency 
region may again be ascribed to cavitation, which is 
the chief source of ship sounds at all but the lowest 
speeds. The sound due to cavitation has a continuous 
spectrum, whereas machinery sound generally is 
more likely to consist of many discrete components 
more or less closely spaced. Above 1 or 2 kc, the 
spectral slope of cavitation sound is very nearly — 6 
db per octave; but in the region of lower frequencies 
there is usually a peak (see Figure 12). The frequecny 
at which this peak occurs depends on various factors 
connected with the type and size of ship and its 
speed, and thus may provide some information tend- 
ing toward identification of the vessel. 

At high speeds, cavitation may introduce compo- 


nents in the supersonic region. This is shown in 
Figure 16 by the curve marked H. 

12 . 5.5 The Distribution of the Sound 
Field around Surface Ships 

The sound emitted by ships has very little direc- 
tivity, particularly in the sonic region of frequencies. 
Average directionality patterns for 15 freighters for 
the low frequencies (200 to 400 c) are illustrated in 
Figure 17 A, where sound levels are exhibited as 
contours, lines joining points of equal intensity. The 
levels were measured with a bottom-mounted hy- 
drophone. 7 

The contours are somewhat difficult to reconcile 
with the observation that many ships have two dom- 
inant sources of sound, one at the engine room, the 
other at the screws. In the case of large destroyers, 
these two sources are of equal level at about 12 knots. 
At 8 knots, the engine room dominates, while at 16 
knots the screws are the dominant source. 8 In Liberty 
ships, however, the two sources are of approximately 
equal level at all speeds. The dominance of the pro- 
pellers as the source of sound for the 15 ships in 
Figure 17 A possibly indicates that the Liberty ships 
are not typical of all freighters. 

If the source of sound from a ship is concentrated 
at the screws or over a small part of its hull, the audi- 
ble sound would be quite independent of direction 
except for the shadow effect of the hull and wake. 
This effect is illustrated graphically in Figure 17B, 
which shows the contours of pressure levels for a 
typical freighter cruising at 8 knots. The outline of 
the ship is shown by the dotted lines. The shadow 
and screening effects are highly variable from ship 
to ship. This, together with the variable distribution 
of the sound sources, makes it difficult to generalize 
about the sound distribution. It is probable that for 
large ships the pressure level 400 to 500 ft ahead or 
astern of the main source of sound is 5 to 10 db below 
the level at the same distance abeam. 7 

12.6 TIME PATTERNS AND 

PROPELLER BEATS 

12.6.1 Rhythms and Other Time Patterns 

The necessary prerequisite for the detection of a 
ship or submarine is that its sound have sufficient 






238 


THE ACOUSTIC OUTPUT OF SHIPS AND SUBMARINES 



Figure 18. Sound spectograms of ships sounds. Time is plotted horizontally, frequency in kilocycles vertically, and 
the spectrum level indicated by the degree of darkening of the print. (A) Spectrogram of supersonic noise from 
medium-sized A/S vessel, twin screws, 5 k. Heterodyned to 800 c; (B) spectrogram of supersonic self noise of S-type 
submarine, speed 3 k at 90-ft depth. Heterodyned to 800 c. 


intensity at the hydrophone to be heard above the 
background noise. Since the level of background 
noise usually varies in an irregular manner, a rhyth- 
mic sound having a periodic pattern of beats, may 
be more readily recognized than a nonrhythmic one. 

Moreover, intensity alone conveys no information 
other than that something in the neighborhood is 
making a noise. Additional information about the 
source is obtained from the spectrum (high or low 
pitch) and from any rhythm that may be inherent 
in the sound. 

The propeller sounds of a large ship, although 
produced by cavitation, usually pulsate periodically. 
In some ships, the beat may be unaccented and occur 
once per propeller revolution (shaft frequency). 
Other propeller sounds pulsate several times per rev- 
olution; a three-blade propeller will give 3, and a 
four-blade, 4 beats per revolution (blade frequency). 
If the beat is unaccented, it is difficult to determine 
which frequency is involved. However, one blade will 
often be noisier than the others, resulting in an accent 
repeated at shaft frequency, while unaccented beats 
dccur at blade frequency. In favorable cases, there- 
fore, both the number of blades and the propeller 
rpm can be determined. These items will partially 
identify the class of ship, and certainly differentiate 
its sound from various intermittent background noises. 

Somewhat similar in its effect on recognition is the 


variation in sound level that can be produced by 
training a directional receiver on and off the target 
in a systematic manner. This, however, contributes 
very little to the identification of ship class. 

Quite dissimilar is the effect of aperiodic fluctua- 
tions in transmission loss. These produce irregular 
variations in sound intensity, and tend to obscure 
any rhythm that may be present in the source. It is 
possible that these fluctuations make ship sounds 
heard at great distances so similar to background 
noise that they are not recognized, even when they 
have an appreciable level. 

12.6.2 Perception of Time Patterns 

The manner in which fluctuations in sound level 
are heard depends on their rate or frequency. Very 
slow changes in level are not perceived unless they 
are relatively large; they are often called “fading.” 
Rhythms are most easily heard and counted when 
the beats occur two or three times a second. At high 
rates, counting becomes difficult; with practice, it 
can be done by counting every third or fourth beat. 
If accented beats are present, this method is easy. 

When the frequency becomes greater than 15 or 20 
per second, the individual beats are no longer heard. 
The rhythm is then heard as a “flutter” or “tremolo.” 



SINGLE -FREQUENCY COMPONENTS 


239 



Figure 19. (A) Spectrogram of sonic noise from a destroyer, speed 15 k; (B) spectrogram of sonic deep sea ambient noise. 


Frequencies much above 100 c are not recognized as 
periodic, but as a pitch that is inherent in the sound. 

12.6.3 Changes in Spectrum 

The time pattern of a sound may consist either of 
changes in level or of spectrum or both. The analysis 
of rapid changes in spectrum requires special equip- 
ment. A sound spectrograph designed by the Bell 
Telephone Laboratories makes it possible to show 
the intensity of the sound as a function of both time 
and frequency. 9 Some spectrograms of noise from 
this analyzer are shown in Figures 18 and 19. Time is 
plotted horizontally, the frequency in kc vertically, 
and the spectrum level is indicated by the degree of 
darkening of the print. Such records are useful in 
giving a qualitative representation of fluctuating 
sound levels. The quantitative analysis of spectral 
fluctuations is still in the incipient stage. 

Figure 18A is an analysis of the sound of a twin- 
screw vessel, as heard with supersonic listening gear. 
Most of the audible output is below 2,000 c, but beats 
of higher-frequency sound occur at a rate of about 
8 c. Figure 18B shows the self-noise of the same gear 
at increased gain and without any signal. The striated 
appearance of the record indicates irregular fluctua- 
tions in the sound. Figure 19 is a pair of records 
obtained with sonic listening gear. 


i2.7 SINGLE-FREQUENCY COMPONENTS 

12 . 7.1 The Audibility of 

Single-Frequency Components 

The discussions of previous sections of this chapter 
have pointed out that ship sounds in general have 
continuous spectra, that is, the emitted sound energy 
is distributed over a more or less wide range of fre- 
quencies, and on the average the distribution of the 
energy over the frequency range follows a fairly 
simple pattern — a decrease in the sound level of 
about 6 db per octave increase in frequency. Mention 
has been made at various times, however, of the 
occurrence in ship sounds of relatively pure tones of 
audible frequency. On a spectrum plot an absolutely 
pure tone would be one-dimensional, having sound 
level but no frequency width; a spectrum composed 
predominantly of such discrete components would be 
a line spectrum. Actually the so-called single-fre- 
quency components comprise a more or less narrow 
band of frequencies; but if the width of this band is 
smaller than the width of the band that can be re- 
solved by ear, it will have a definite pitch. It is in 
this sense that the terms “single-frequency compo- 
nent” and “pure tone” are used. 

The ear very readily detects pure tones against a 
background of complex noise. This is possible because 




240 


THE ACOUSTIC OUTPUT OF SHIPS AND SUBMARINES 



«• u«3 » souiid f o mw ro>» ». mi. ios 





Figure 20. Power-level record of a 550-c component 
in the sounds from a carrier. The periodically recurring 
variation in average intensity is apparent. An entirely 
comparable trace from a second carrier of the same 
class, but fitted with different propellers, is shown in 
the lower half of the figure. This sound has a random 
pattern and a lower level than the former. 

the ear is a very efficient analyzer of comparatively 
high selectivity, and because a pure tone has a dis- 
, tinctive quality that contrasts strongly with random 
noise, which has no definite pitch. These character- 
istics make it possible for the ear to detect a pure 
tone in the audible region even when its sound level 
is considerably lower (sometimes as much as 20 db) 
than the overall level of the background noise. Tests 
have shown that a pure tone can be heard when its 




X *cc , 



* screufs SO *PM 


Figure 21. Oscillogram of 220-c component in the 
sound of a submarine running on two screws. The beats 
may be due to different shaft rates of the two screws. 

level is at least equal to the level of the background 
noise in a band of a certain width at the frequency of 
the tone. The width of the band depends on the fre- 
quency. These critical bands are from 30 to 50 c wide 
for tones between 100 and 1,000 c; this gives an 
indication of the great effectiveness of the ear in 
discriminating against random noise. This topic will 
be dealt with more fully in Chapter 14. 

12 7.2 Time Patterns of 

Single-Frequency Components 

It sometimes happens that pronounced rhythmic 
time patterns occur in single-frequency components 
originating in propeller vibrations. An example of 
this effect is shown in the upper part of Figure 20, 
which is a power-level record of a 550-c component in 
the sounds from a carrier. The periodically recurring 
variation in average intensity is quite apparent. An 
entirely comparable trace from a second carrier of 
the same class, but fitted with different propellers, 
is shown in the lower half of the figure. It is seen that 
this sound has a random time pattern with no dis- 
cernible periodicity, and considerably lower level. 

A rhythmic time pattern in the case of single- 
frequency components may originate in another way. 
Many single-frequency components have their source 
in the reduction gears. If a ship has twin screws, the 
two propellers may have slightly different shaft rates. 
This would result in the reduction gears’ producing 
two tones that differ only by a few cycles per second. 
In this case one would perceive fluctuations in result- 
ant level, as the two tones came in and out of phase. 

The oscillogram shown in Figure 21 may be an 
example of this effect. The figure is the trace of a 


SINGLE-FREQUENCY COMPONENTS 


241 


FREQUENCY, CPS 

tOO 500 100 0 











• w 

= 300 C 

PS 

























w 

= 30 cp: 

5 


r 

1 






















w 

= 5 CPS 


















Figure 22. Schematic illustrating the measurement of 
the level of a single-frequency component. 


f, FREQUENCY, KC 



Figure 23. Spectrum of the sound whose time pattern 
is shown in Figure 21. Because of the difficulties in 
measurement, the single-frequency component is shown 
as a dotted line. 


record of the variation of the sound level with time 
of a 220-c component in the sound of a submarine 
running on two screws. The trace shows a well- 
defined periodic fluctuation, but the frequency of the 
fluctuation changes; during some time intervals there 
are 3 or 4 per second ; during others they may occur 
as slowly as 1 per second. It is evident, therefore, that 
they are not due to simple propeller modulations, 
which would be regular. The variation in the rate at 
which the beats occur is probably due to a small 
variation in the shaft rates. 

The extreme audibility of single-frequency com- 
ponents, as compared to sounds of continuous spec- 
trum, introduces complications into the techniques 
of sound measurement. For example, suppose the 
overall level of a submarine is being measured at 
dock, and that, with a motor secured, it has a con- 
tinuous spectrum of certain overall level. The motor 
may produce a pure tone which increases the audi- 
bility of the submarine’s sound very materially, but 
may scarcely affect the overall level. 

In order to obtain reliable measurements of single- 
frequency components, the spectrum level must be 
determined with a system using a very narrow filter. 
Even then corrections for the bandwidth must be 
applied. To see this, suppose the spectrum level of a 
sound is S and that a pure tone of level L can be 
turned on or off at will. Let 

S = 10 log I h 

L = 10 log I, 

and let both be measured with a system having the 


bandwidth w. The power output in the absence of 
the pure tone will be 

P = hw , 

and when the pure tone is added, will be 
P' = hw + 7. 

If the system is calibrated in spectrum-level units, 
the meter reading corresponding to P will be S and 
that corresponding to P r will be S + s = 10 log P'. 
Hence 

s = ioi ° g (i+LJ. 

As w becomes very great, s will approach zero. 

It will be shown in Chapter 14 that the ear behaves 
like such a system, with a bandwidth w c = 30 to 50 c 
over most of the audible range. As explained above, 
w c is called the critical band of the ear. It is found 
that the pure tone will just be audible above the 
background when I = w c I i. The increase in meter 
reading caused by the pure tone at this level is thus 

/ w c 

s 0 = 10 log ( H 

\ w 

If w c = 30 c and w = 300, the increased reading will 
be only s 0 = 0.4 db. If w is reduced to 30 c, the in- 
creased reading due to the pure tone will be 3 db; 
and if w = 5 c, s 0 = 8.5 db. 

These considerations are illustrated in Figure 22, 
which shows, in idealized form, the uncorrected spec- 
tra obtained with three analyzers using different 
pass bands. All three are supposed to be applied to 
the same sound, which has a continuous spectrum 




242 


THE ACOUSTIC OUTPUT OF SHIPS AND SUBMARINES 


FREQUENCY, CPS 

0 200 400 600 800 I OOP 


1 




•AVERAGE CURVE 

AREA COVERED BY 
RECORDER TRACE 








J 







4 





















CxT 








Figure 24. Spectrum of a submarine. The heavy line 
was obtained with an analyzer using a wide band; the 
analysis with a narrow filter shows many sharp peaks. 


plus an audible single-frequency component at 600 c. 
In actual practice, the graphs will not be so simple 
for various reasons. The filter edges will not be sharp, 
and the time patterns of the sound levels cause the 
graphs to be irregular lines rather than straight. 


Figure 23 shows the spectrum of the sound whose 
time pattern is shown in Figure 21. Because of the 
difficulties in measurement, the single-frequency com- 
ponent is shown as a dotted line. Its level is probably 
35 db above the level of the other ship sounds. It was 
distinctly audible as a whine. Similar screw sounds 
have been heard over distances of 30 miles. Yet the 
contribution of this whine to the overall level of the 
sound output was very small. The importance of 
spectral analyses (even if only made by ear by a 
trained listener) in supplementing overall level meas- 
urements cannot be overemphasized. 

As a further example, Figure 24 shows the spectrum 
of a submarine’s sound. The heavy line was obtained 
with an analyzer using a wide band, and shows no 
values above 20 db. The analysis with a narrow 
filter shows many sharp peaks, several of which rise 
above 40 db. These, together with the marked time 
pattern, indicated by the shaded area, make this 
submarine far more vulnerable to detection than 
would be thought from a consideration of the solid 
line alone. 


Chapter 13 

BACKGROUND NOISE 


13.1 BACKGROUND NOISE IN GENERAL 

13.1.1 Airborne Noise 

I n listening the operator depends almost entirely 
on his ears, unaided by any form of recorder, etc. 
Occasionally, a decibel meter or “magic eye” may be 
available for supplementary quantitative informa- 
tion. His task reduces to detecting and recognizing a 
wanted signal against the background of all the other 
sounds that impinge on his ear. They are many and 
complex. As a first step in the discrimination process, 
the operator will distinguish between the sounds that 
are airborne from his surroundings, and those that 
issue from the loudspeaker or headphones, and 
have been picked up or generated by the receiver 
system. Airborne sounds may, in some cases, be a 
limiting factor. Listening in an airplane for the sig- 
nals of a radio sono buoy is sometimes limited by this 
type of noise, which is often referred to as “local 
noise” or “room noise.” 

Against airborne noise, the signal can be made 
more perceptible by increasing the amplification of 
the receiver; for in this case the background noise is 
not amplified, and the signal-to-noise ratio will be 
increased. 

13.1.2 Amplified Noise 

The wanted signal is only one among many different 
sounds that are incident on the hydrophone, and that 
originate in the sea and in the listening vessel itself. 
These sounds constitute a masking background for 
the signal. Increasing the gain of the amplifier system 
obviously does not benefit in this case, for the back- 
ground noise will be amplified together with the 
signal, and the signal-to-noise ratio will not be 
improved. 

Finally, as has already been discussed in Chapter 
9, the receiver system itself is a source of noise volt- 
ages, which are amplified and converted into sound, 
and these sounds form a part of the masking back- 
ground noise against which the signal must be de- 
tected. Again, in this case, increasing the gain will 


increase the noise as well as the signal, and will not 
increase the signal-to-noise ratio. 

All of the amplified background noise is distributed 
over a considerable frequency band, although in bad 
cases 60-c hum may dominate. The first principle for 
obtaining a good signal-to-noise ratio is that the 
frequency band to which the receiver is made to 
respond be no wider than is necessary to accommodate 
the signal; for the intensity of the background noise 
emitted by the loudspeaker is roughly proportional 
to the bandwidth in which it is received. Unfortu- 
nately, the wanted sounds or signals are also wide 
band. Their spectra do not differ in any systematic 
way from those of the background. Consequently 
the application of the principle is not very simple in 
this case. 

13.1.3 The Classification of Amplified 
Background Noise 

Because of the diversity and complexity of the 
sounds that make up the background noise, it is 
convenient to have a more or less rigorous termin- 
ology. A classification of background noise was given 
in Section 9.2. In Figure 1 essentially the same classi- 
fication of background noise is submitted in diagram- 
matic form. It will be convenient to summarize the 
discussion again before taking up the several kinds 
of noise in detail. 

The amplified noises are classified according to 
their physical origin into (1) self-noise, the sounds 
originating in the listening vessel and the receiver 
system; and (2) ambient noise, the sounds inherent 
in the sea itself, which would be detected by even a 
perfectly noiseless stationary receiver. 

The sources of self-noise are threefold: 

1. In the absence of all other sound the receiver 
system itself generates noise. This is called circuit 
noise. 

2. The hydrophone may be caused to vibrate by 
motion through the water, and thus sound will be 
emitted from it and from its housing and will be 
directly translated to electrical impulses. 

3. The ship sounds from the listening vessel itself 
tend to mask the sounds from possible targets. 


243 


244 


BACKGROUND NOISE 


BACKGROUND 

NOISE 


AMPLIFIED NOISE 


SELF NOISE 



[circuit noise 



HYDROPHONE 

MOTION 



NOISE FROM 
OWN SHIP 


AMBIENT NOISE 



SEA NOISE 



BIOLOGICAL 
^ NOISE 



TRAFFIC NOISE 



SPEECH 


AIRBORNE NOISE 


b 

OTHER SONAR 
GEAR 



GUNFIRE 


I" igure 1. Classification of background noise. 


The sources of ambient noise are also threefold : 

1. Sea noise, caused by the action of the wind and 
weather, the patter of rain and hail, etc. 

2. Biological noise, produced by various species of 
marine animals. 

3. As distinct from the natural sources mentioned 
in 1 and 2, one encounters unwanted sounds from 
man-made sources whose character depends strongly 
on locality. They include passing ships, industrial 
establishments on shore, the incidental underwater 
sounds of battle, etc. These are designated traffic 
noise, for want of a better term. 

It will be noted that in this classification no pro- 
vision is made for including reverberation in the 
background noise. It is evident that since in listening 
no ping is transmitted, there will be no reverberation. 
If the target vessel projects pings, and these are 
received by a listening device, the pings themselves 
as well as the forward reverberation, if any, resulting 
from the pinging, will form part of the wanted signal 
sounds and hence are not part of the background. 

In echo ranging, on the other hand, reverberation 
is likely to be the most important factor in the un- 
wanted background noise. The masking properties 
of reverberation have been discussed in connection 
with echo ranging (Chapter 10). For the simplifica- 


tion of an essentially complicated subject like back- 
ground noise, it seems advisable to omit reverbera- 
tion from a classification of background noise. 

13.1.4 Summary of Overall Levels of 
Amplified Background Noise 

Table 1 is a summary of average values of back- 
ground noise of different kinds. These values are 


Table 1 . Overall levels of amplified noise (0.1 to 10 kc). 


Self-noise 

Decibels 

Circuit noise 

- 30 to 0 

Submarine self-noise 

0 to 20 

Surface vessel self-noise 
(DD or DE) 10 to 25 knots 

5 to 40 

Ambient noise 


Sea noise 

Deep sea 

Near surface 

— 5 to 6 
- 17 to 9 

Biological noise 

Snapping shrimp 

Croakers 

Porpoises 

Evening noise 

Traffic noise (includes sea noise) 

5 to 7.5 
36 (max) 
40 (max) 
8.5 (max) 

0 to 22 







CIRCUIT NOISE 


245 


FREQUENCY, KC 



Figure 2. Spectrum of circuit noise (dotted curve). 
The spectrum of sea noise as measured with this system 
is also drawn in for comparison. The circuit noise level 
is seen to be from 10 to 12 db below that of sea noise 
on this occasion, but the two curves are roughly parallel. 

approximate. It is apparent that since the sources of 
specific kinds of noise cannot always be isolated, 
values assigned to them are based on estimates. As 
an instance, traffic noise cannot be measured distinct 
from other ambient noise, and the noise due to 
hydrophone motion is necessarily included in a meas- 
urement of the self-noise produced by the ship on 
which it is mounted. 


is 2 CIRCUIT NOISE 

i3.2.i Sources of Circuit Noise 

An acoustic receiver converts sound pressures into 
electric impulses, amplifies these, and finally portrays 
them in some manner that makes them perceptible 
to the operator. Each of these three functions has its 
own distinctive set of problems. The present discus- 
sion is concerned primarily with the perception of 
sounds; it deals with the other two functions only as 
they affect the perceptibility of the sound incident on 
the hydrophone. It is from this viewpoint that circuit 
noise is discussed here. 

Circuit noise has been mentioned as being an 
important factor in determining the threshold of a 
receiver system (Section 12.3). It is important in two 
respects: it contributes to the total of background 


noise, and it sets a definite limit to the number of 
stages of amplification that can be used. Any slight 
change in the currents flowing in the plate or heater 
circuit of an amplifier tube, especially if it is one of 
the first tubes, will be amplified and may finally 
produce a very large change in the plate current of 
the last tube and a consequent loud click in the 
loudspeaker. If these changes occur with sufficient 
frequency, the result may overload the tubes in the 
last stage of amplification. Even before this state is 
reached, the noise may completely hide the wanted 
sound, thus making additional stages of amplification 
useless. 

The spectrum of circuit noise of a certain receiving 
system is shown in Figure 2. 1 The spectrum of sea 
noise as measured with this system is also drawn in 
for comparison. It is seen that the spectrum level of 
the instrument noise was from 10 to 12 db below that 
of the sea noise on this occasion, but that the two 
curves are roughly parallel. The overall level of the 
circuit noise is about — 10 db. 

The sources of circuit noise are (1) the thermal 
agitation of electrons in the tuned input circuit, 
(2) tube noise, (3) hum due to man-made disturb- 
ances of various kinds, (4) mechanical vibration of 
the elements of the tube, resulting in “microphonics.” 

It will be recalled (Section 12.2) that it is circuit 
noise which, together with the response of a hydro- 
phone, determines the receiving threshold of a 
receiver. 


13 2.2 Thermal Noise 

Thermal noise is unavoidable in a receiver circuit. 
A conductor will show a fluctuation of potential be-r 
tween its terminals even when no external source of 
voltage is applied to it. This fluctuating potential is 
due to the thermal agitation of the electrons in the 
conductor, a phenomenon analogous to the thermal 
agitation of molecules in matter. 

The frequency of fluctuation of this thermally 
generated voltage ranges from zero to frequencies 
higher than any used in communication. The sound 
that results when the voltages are amplified and sent 
through a loudspeaker therefore has a continuous 
spectrum. 

The magnitude of the thermally generated voltage 
is determined by the resistance and temperature of 
the conductor, and for a given conductor the mean- 
square voltage is proportional to the width of the 


246 


BACKGROUND NOISE 


frequency band over which the voltage is measured. 2 * 
These thermal voltages set a lower limit to the small- 
est voltage, resulting from sound incident on the 
hydrophone, that can be amplified without being lost 
in a background of noise. In other words, the ultimate 
limit of signal-to-noise ratio (restricting the term 
“noise” in this connection to circuit noise) is obtained 
when (1) the receiver bandwidth has the minimum 
possible value and (2) all the noise in the receiver 
output is caused by thermal agitation in the input 
circuit to the first tube of the amplification system. It 
should be added that while this limit is determined 
by the width of the band that is being amplified, it 
is not affected by the position in the frequency spec- 
trum at which the band is located. 

It need hardly be said that the ultimate limit of 
signal-to-noise ratio just described is never attained 
in practice. It is impossible to eliminate all other 
circuit noise except under very carefully controlled 
laboratory conditions. 


13.2.3 Tube Noise 

Tube noises have their source in fluctuation in the 
currents associated with the electrodes of the tube. 
These fluctuations also are amplified and result in 
spurious voltages that contribute to the circuit noise. 
Usually tube noise, rather than thermal noise, sets 
the lower limit to the voltage that can be amplified 
without being completely masked. 

Tube noise differs from thermal noise in that it can 
be controlled or reduced to a certain extent by proper 
design and construction of tubes. 


13.2.4 Hum 

Man-made electrical disturbances are responsible 
for the third class of circuit noises, generally desig- 
nated hum. The chief source of hum is found in poorly 
filtered power supply systems, and in stray magnetic 
fields resulting from faulty transformers. Currents 
of the power frequency and its harmonics introduced 
into the amplifier circuits in the low-level stages may 
be amplified and thus become troublesome, partic- 
ularly in high-gain audio-frequency amplification. 

Hum can be controlled by intelligent design of 
circuits, proper electric and magnetic shielding, and 
careful design and installation of the electric grounds 
of both sonar and other gear aboard ship. 


13.2 5 Microphonics 

Mechanical vibrations of parts of circuits associ- 
ated with the amplifier tube will modulate the voltages 
being amplified. This will result in a circuit noise 
called “microphonics.” The mechanical vibrations 
may be the result of vibrations of the receiver unit or 
even of the vessel containing it, or they may result 
from the direct mechanical action of the sound waves 
issuing from the loudspeaker. The control and elim- 
ination of microphonics evidently is obtained by rigid 
construction of the affected circuit element, by re- 
ducing vibration of the whole unit by shock-mounting, 
and finally by protecting the unit against the direct 
action of sound waves. 

13.3 OTHER SELF-NOISE 

13 .3.1 Sources of Self-Noise 

If it were possible to construct a hydrophone that 
generated no circuit noise and if this hydrophone 
were placed in water that was absolutely silent, it 
would record no sound if it were kept stationary. But 
if it were moved through the water, the motion would 
cause vibration of the diaphragm, resulting in am- 
plified noise. 

If the hydrophone is mounted on a ship, it is 
probable that it encounters air bubbles in the water 
under the ship, and their impact on the hydrophone 
will increase the noise. Moreover, the sounds emitted 
by the vessel would be added to the sounds incident 
on the hydrophone; and there would be the inter- 
mittent noise due to the slapping of waves against 
the hull. 

13.3 2 The Character of Self-Noise 

If listening is being done on board a moving ship, 
the noise of the ship itself is probably the chief source 
of self-noise. Ship sounds were discussed in detail in 
Chapter 12. It was stated there that at low speeds 
the noise originated mainly in the machinery and 
that, as the speed increases to a certain critical value, 
cavitation sets in and the level of the ship noise 
rises abruptly. 

Another important source of self-noise in the case 
of listening from surface vessels is turbulence at the 


BACKGROUND NOISE 


247 


FREQUENCY, KC 


10 


20 30 40 50 60 80 100 



FREQUENCY, KC 



Figure 3. (A) Spectra of supersonic self-noise of a submarine at various speeds and depths. 3 (B) Spectra 
of supersonic self-noise of submarines submerged at periscope depth at 8 knots. 6 


Curve 

Symbol 

Ship 

1 

X 

Cavalla 

2 

□ 

Pipefish 

3 

0 

Average of the five 

4 

A 

Sea Lion 

5 

• 

Shark 

6 

V 

Tarpon 


hydrophone. Entrained air bubbles were mentioned 
above. The effects of both can be mitigated by en- 
closing the projector head in a streamlined dome. 

The high level of self-noise on surface vessels makes 
listening less useful there than on submarines. For 
this reason most observations of self-noise have been 
made on the latter, and very little is known quan- 
titatively concerning self-noise of surface vessels. 

A listener on a submarine has described his impres- 
sion of the self-noise as follows. 

1. A random noise, apparently not related to the 
motion of the submarine, together with steady whines. 

2. Short bursts of sound which occur at the blade 
rate. 

3. A swishing sound occurring at the rotation rate 
of the shaft. 

4. A steady hiss in addition to the preceding inter- 
mittent sounds. 

These observations as well as others suggest that 
it is a composite of three effects. 

1. A fixed background noise that is independent 
of the speed of the vessel, probably circuit noise with 
added ambient noise. This may decrease somewhat 
with depth. 

2. Self-noise proportional to the speed. 

3. Cavitation noise. 

As stated in the previous chapter, the speed at 
which the submarine begins to cavitate depends on 
the depth of submergence. 

The characteristic quantitative features of self- 


noise are shown in Figures 3 3 6 and 4. 4 6 The data 
given in these figures are expressed in terms of rms 
pressure of a plane wave in the water, the direction 
of which is parallel to the acoustic axis of the hydro- 
phone. This differs from the general convention in 
regard to noise as adopted elsewhere in this book, 
according to which the results of measurement are 
expressed in terms of equivalent isotropic noise. The 
relation between the noise level in terms of the plane 
wave convention N and the level N t in terms of the 
isotropic convention is given by 

N = N i + D, 

where D is the directivity index of the hydrophone. 

Figure 3A shows how the spectrum level of self- 
noise of supersonic frequencies varies with ship speed 
in the case of a submerged submarine. The spread in 
the self-noise levels of different submarines is shown 
by Figure 3B, which shows the supersonic spectra of 
the self-noise of five different submarines traveling 
at 8 knots at periscope depth. It is seen that there 
may be as much as 30 db difference in the spectrum 
levels of the self-noise of different submarines. Fig- 
ure 4A shows the spectra, for sonic frequencies, of the 
self-noise of a submarine at periscope depth for speeds 
of 2, 4, and 8 knots. Figures 4B and C compare the 
self-noise in the sonic band of frequencies (0.1 to 
10 kc) with that at 24 kc; in this figure the overall 
sound level is reduced to an equivalent spectrum 


248 


BACKGROUND NOISE 


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Figure 4A. Spectra of sonic self-noise of a submarine 
at various speeds, submerged at periscope depth. 6 
B. Variation with shaft rate of equivalent 5-kc spec- 
trum level of sonic self noise of a submarine. C. Same as 
Figure 4B for supersonic self-noise. 4 


level (1-c band) centered at 5 kc, and this is plotted 
against shaft rate for several depths. It is seen that 
the corresponding supersonic and sonic curves are 
quite comparable in shape. 

The directionality of high-frequency self-noise of a 
submarine is shown in Figure 5. The level of the self- 
noise in a 1-c band at 24 kc is plotted for various 
relative bearings of the directional hydrophone. 



It will be seen from Figure 5 that at low speeds the 
self-noise is practically nondirectional. As the speed 
increases from 4 to 7.6 knots, the self-noise from 
dead astern (180 degrees) increases more than 30 db. 
This increase is due to cavitation, which sets in at a 
speed of about 6 knots. 


is 4 AMBIENT NOISE 


13.4.1 Sources of Ambient Noise 

If a hypothetical, perfectly noiseless, stationary 
receiver were placed in the sea, it would convey to 
a listener many diverse sounds. The ocean is by no 
means a region of silence. It is never at rest, and the 
splashing of the water as it encounters solid objects 
and the breaking of waves generate noise. Many 
forms of marine life produce characteristic sounds, 
and at times such sounds may swell into a chorus. 
Near cities and harbors industrial noise may be trans- 
mitted by the sea, and ship traffic and underwater 
sounds incident to battle may add their contribution. 
All the various noises associated with, or resident in, 



SEA NOISE 


249 


the sea itself, as distinct from self-noise, are collec- 
tively designated by the term ‘ ‘ambient noise.” 
Corresponding to the chief agents just mentioned, 
ambient noise. is classified into three categories: (1) 
sea noise, due to wind action, rain, and hail; (2) bio- 
logical noise, due to marine life; (3) traffic noise, due 
to man-made conditions. 

These three classes of ambient noise are taken up 
in some detail in the succeeding sections. It is worthy 
of mention that little underwater sound can be pro- 
duced by sources in the air itself. The air-water 
surface reflects most of the sound incident on it from 
either side, and transmits so little that it can be 
neglected for practical purposes. 

13.4.2 The General Character of 
Ambient Noise 

The outstanding characteristic of ambient noise 
is its great variability. At a given locality one or 
another of the three classes just mentioned may be 
the dominating one. In the open deep sea it will 
likely be chiefly sea noise; in or near harbors, traffic 


WAVE HEIGHT, CREST TO TROUGH, FT 
.05 0.1 0.2 0.3 0.5 IJD 2.0 3.0 5.0 10.0 20.0 50.0 



Figure 6. (Top) Sea noise, overall level (0.1 to 10 kc) 
as a function of wave height. The Weather Bureau 
sea scale is inserted. ( Bottom ) Overall level of sea noise as a 
function of wind velocity. The Beaufort scale is shown. 


noise; near certain coasts various forms of marine 
life may be the main contributors. Or the ambient 
noise may be composed at the same time of two or of 
all three of the classes more or less equally presented. 

Besides the variability in the quality of ambient 
noise from place to place, the listener at a given 
locality will observe considerable fluctuations in its 
intensity; for the range and bearing of a localized 
source will probably change, as for example in the 
case of passing ships or a school of musically inclined 
fish. The transmission of sound in the sea is subject 
to changes, which affect the number of sources that 
contribute to the ambient noise at a given place. 
Finally, the sources of ambient noise themselves 
exhibit definite diurnal and seasonal variation. 

For all these reasons ambient noise cannot be 
specified as a definite, constant quantity, but must 
be described in statistical terms ; that is, an estimate 
can be made of the most probable or average amount 
of noise which is to be expected under given circum- 
stances. In addition, it is frequently possible to esti- 
mate the degree of variability in terms of a fre- 
quency distribution or of the standard deviation of 
the distribution, when the distribution is known to 
follow the normal law. 

13.5 SEA NOISE 

13.5.1 Sea Noise due to Wind Action 

Sea noise usually is the prevailing form of ambient 
noise in open and deep water but may also dominate 
in shallow water. It is produced mainly by the agita- 
tion of the sea surface, and hence is related to wind 
strength and sea state. Most observers conclude that 
it is chiefly breaking wave crests at the sea surface that 
produce sea noise, and that very little sound is gen- 
erated by the unbroken undulations of the surface. 

The dependence of sea noise on sea state is illus- 
trated in Figure 6 where the overall sound level, 
(0.1 to 10 kc), is plotted against sea state and wind 
velocity. The wave heights are estimated by eye. 
These graphs represent average values, and con- 
siderable deviation from them can be expected. 

13.5.2 Spectra of Sea Noise 

Sea noise has its energy distributed chiefly over 
the sonic band. Average spectrum levels to be ex- 



250 


BACKGROUND NOISE 



pected under various conditions of sea state and 
wind force are shown in the graph of Figure 7. It is 
interesting to note that the sea state appears to have 
no systematic effect on the average spectral distri- 
bution of sea noise ; consequently all the curves show 
a uniform decrease of noise level with frequency 
amounting to about 5 db per octave. On any specific 
occasion, appreciable random departures from the 
curves are to be expected. 

Deep-sea noise is presumed to be isotropic, i.e., to 
come equally from all directions, for neither the over- 
all noise level nor the spectrum levels are dependent 
on depth. However, the character of the noise is 
different at different depths. Near the surface the 
noise from individual waves can be discerned, and 
the fluctuations in the noise level are more pro- 
nounced there than they are at greater depths. 

13.5.3 Other Sources of Sea Noise 

The thermal agitation of the water molecules, 
sometimes called “water noise,” produces sound of 
intensity equal to that caused by the thermal agita- 
tion of electrons in the first input stage of the receiver 
system and is indistinguishable from the latter. The 
level of sea noise actually observed, even when the 


sea is very calm, is of a much higher level than this 
thermal noise. 

Rain and hail undoubtedly cause noise, but no 
quantitative data are available on this subject. It 
has been informally reported that at New London a 
rise of 20 db in the overall noise level was observed 
during a heavy but not torrential rainstorm. 

The contribution of surf noise has been measured. 
It was observed that the overall sound level, meas- 
ured near the bottom 300 yd offshore, during “rough 
weather” was 4 db. This corresponds to deep-sea 
conditions of sea state 4 and wind force 4 to 5, ac- 
cording to Figure 6. 

It is possible that the movement of bottom material 
may contribute to sea noise near shore, although 
there is little evidence of such movement on a scale 
large enough to be a significant factor in noise pro- 
duction. No measurements have been attempted. 

13.6 BIOLOGICAL NOISE 

13.6 i Sources of Biological Noise 

Surprisingly large numbers of different species of 
marine life can and do produce sounds of various 


BIOLOGICAL NOISE 


251 



DISTRIBUTION OF SNAPPING SHRIMP 

Figure 8. The distribution of snapping shrimp. Shaded areas show regions where shrimp occur when water depth and 
bottom character are favorable. 


sorts. They are mostly crustaceans and vertebrates. 
Biological noise is an important factor in limiting 
listening ranges in shallow water only in tropical and 
subtropical regions. To discuss the complicated sub- 
ject conveniently, it is customary to group the var- 
ious sounds from marine life into three categories, 
which in the order of their importance from an 
operational viewpoint are (1) shrimp noise, (2) per- 
iodic fish choruses or croaker noise, (3) miscellaneous 
biological noise. 


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13.6.2 Shrimp Noise 

Early in World War II, it was observed that as 
one approached shallow water, the ordinary ambient 
noise was sometimes replaced by sounds resembling 
the sizzle of frying fat; on coming closer to the shore, 
the sound approximated the crackle of burning twigs 
or the crashes of static noise heard in a radio receiver. 
This noise was encountered only in tropical and sub- 
tropical regions, and it was observed to be more 
common over rocky boulder- or cobble-strewn bot- 
toms. It was sometimes confused with noise due to 
surf. Investigation discovered the source of this noise 
to be colonies of certain species of snapping shrimp 
(not to be confused with the ordinary edible species) 
that close their pincers with a loud audible click, 
similar to that which can be caused by snapping a 


FREQUENCY, KC 



Figure 9. Spectra of shrimp noise for daytime and 
nighttime. The dots indicate average values; the dotted 
curves show the spread of the spectrum levels. 


fingernail. The rate at which a single shrimp produces 
clicks and the reason for this activity is not known. 
The combined activity of hundreds of thousands of 



252 


BACKGROUND NOISE 



Figure 10. Diurnal variation of shrimp noise, over- 
all level at various locations. 


is a serious complication in both sonic and supersonic 
listening. 

Directly over a shrimp bed the sound output of a 
directional hydrophone appears to be independent 
of the hydrophone orientation, both in the horizontal 
and vertical directions. It is also independent of the 
depth of the hydrophone. At the edge of or at a 
distance from the bed the noise level depends very 
strongly on the hydrophone bearing. 

Shrimp noise is remarkably constant throughout 
the year, no appreciable seasonal variation having 
been observed. There is a small diurnal variation: 
the noise is from 2 to 6 db higher at night than in 
the daytime, small maxima occurring about an hour 
before sunrise and after sunset (see Figure 10). 


13 6.3 Periodic Fish Choruses 


MONTH TIME OF DAY 



the animals is required to produce the observed sizzle. 
They are very widespread all over the world in trop- 
ical and subtropical regions (see the map shown in 
Figure 8.) Their habitat is rocky sea bottom in water 
less than 30 fathoms deep. Few are found on mud or 
sand bottom, but coral is a very favorable environ- 
ment. 

Shrimp noise is a serious masking noise in listening, 
both because of its intensity and because of its spec- 
tral distribution. While it has a measured frequency 
range of 1.5 to 45 kc, the main components lie be- 
tween 1.5 and 20 kc. The spectrum level at 10 kc 
may be of the order of - 39 to - 29 db, as can be 
seen from Figure 9. It is evident that shrimp noise 


The chief noise makers among fish are found in 
certain species of croakers and drumfish, which are 
common, especially on the Atlantic Coast. An in- 
dividual croaker emits sounds resembling 4 to 7 
rapid blows on a hollow log. 

At certain periods of the year, large schools of 
croakers infest certain localities: in the Chesapeake 
Bay the croaker season extends from May to July. 
During this season there is an evening chorus of 
croaker noise lasting several hours, with a peak just 


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show the difference in average level between early 
evening and the period after midnight during July. 
The dotted curve is the average spectrum for early June. 


TRAFFIC INOISE 


253 


after sundown. Overall levels of croaker noise show- 
ing seasonal and diurnal variation are shown in 
Figure 11. 

The spectrum levels of a sample of croaker noise 
are shown in Figure 12. When it occurs, croaker noise 
may completely mask wanted signals, for the fre- 
quency range lies almost entirely below 1 kc, the 
region where the most prominent components of 
ship sounds occur. 

13.6.4 Miscellaneous Biological Noises 

Besides the crackle of shrimp in some regions and 
the daily chorus of croakers in others, the sonar 
operator will hear at various times an assortment of 
clicks, squeaks, honks, groans, barks, gobbles, whis- 
tles, beats, or moans, all of which doubtless have 
their origin in some form of marine life. Drumfish, 
groupers, crabs, lobsters, pompano, porpoises, sea 
lions, seals, and sea robins have all been identified 
as active members of the marine band. As a rule, 
these sounds are not very important factors in mask- 
ing wanted sounds. 

One of the few of these miscellaneous noises that 
have been investigated to any extent is a noise en- 
countered at Oahu, T. H., and at Midway Island. It 
occurs from about sunset to midnight and resembles 
the discordant sound of a peanut vendor’s whistle. 
It is a serious factor in limiting sonic listening ranges ; 
the frequency range is around 3 kc, and its level is 
about 15 db above the normal background noise. 
This noise is referred to as “evening noise” in the 
literature and should not be confused with the 
“evening chorus” of the croakers. Overall sound levels 
of ambient noise measured at Pearl Harbor, showing 
the occurrence of evening noise, are given in Figure 13. 


TIME OF DAY 

0000 0600 1200 1800 2400 



Figure 13. Overall level of ambient noise for 1 day, 
showing “evening noise.” 


FREQUENCY, KC 



Figure 14. Spectra of traffic noise in New York Harbor 
and its approaches during the daytime. Curve A is 
the spectrum of the noise in the harbor, Curve B the 
average levels measured in upper Long Island Sound 
near the ship lanes. Curve C is the spectrum of sea 
noise for sea state 2, included for comparison. 

FREQUENCY, KC 



Figure 15. Same as Fig. 14, but for nighttime. The 
average daytime spectrum is shown by the dotted curve. 


is ? TRAFFIC NOISE 

In and near busy harbors, the ordinary sea noise 
(and biological noises if present) are overlaid with 
the sounds associated with the movements of ships, 
especially small high-speed craft, and by the noise 
of industrial operations on the beach. Listening in 
harbors thus becomes extremely difficult; hence in- 
stallations off the harbor entrance have been devised 
to ensure protection for harbors against the sneak 
attacks of enemy submarines. 

Traffic noise is essentially variable, but a certain 
periodicity is to be expected. Measurements made in 
New York Harbor and its approaches are shown in 
Figure 14. Curve A shows the spectrum level of the 
noise in the harbor in the daytime, and curve B the 
average levels measured in upper Long Island Sound 
near the ship lanes. The latter is seen to be about 8 


254 


BACKGROUND NOISE 


to 10 db below the harbor level at all frequencies. 
For comparison, the curve of sea noise for sea state 2 
is included as curve C. In the region of sonic fre- 
quencies the harbor noise is seen to be from 10 to 18 
db above this level. Overall sound levels (0.1 to 10 
kc) for the noise in the harbor itself is about 16 db, 


compared with 6 db in the harbor approaches, and 
0 db for water noise with sea state 2. 

Nighttime levels of ambient noise in New York 
Harbor approaches are shown in Figure 15 with a 
curve showing average daytime levels added for 
comparison. 




Chapter 14 


HEARING AND RECOGNITION 


h i THE HUMAN EAR 


14.1.1 Introduction 

C onfusion sometimes arises between the objec- 
tive physical phenomenon of sound and its 
subjective perception by a listener. The reader is 
doubtless familiar with a philosophical problem that 
agitated the ancients, which was formulated some- 
what as follows. A tree crashes in the middle of a 
forest, and no living being is present to perceive the 
fact. Was there any sound? 

Most of the lengthy arguments that were expended 
on this question could have been avoided had there 
been adequate theories of sound and hearing. Today 
sound means waves, which travel in the air, water, 
or other medium. Thus the answer to the question is 
yes. Sound is to be distinguished from the sensation 
of hearing, or auditory sensation, which is a phenom- 
enon occurring in a human being or animal. There 
was no auditory sensation in the above example. In 
order to clarify the distinction between the sensation 
produced by a sound, and the sound itself, the latter 
is often called the stimulus. This is a useful word, 
for supersonic waves are sound, but they do not 
stimulate the sensation of hearing in human beings ; 
they are thus not a stimulus of auditory sensation. 

The most elaborate listening gear is useless unless 
there is an operator to hear and interpret the sound 
waves produced by its loudspeaker. The capabilities 
and limitations of the operator whose task it is to 
interpret the sounds issuing from the listening gear 
are important in determining the success or failure 
of its mission. For this reason, the present chapter 
on the physics, physiology, and psychology of hear- 
ing is included, even though it is not strictly a part 
of the theory of underwater sound. Throughout this 
chapter, the subject matter will be airborne sound. 
This is not to say that a diver cannot hear when 
completely submerged in water; but this aspect of 
underwater sound will be ignored. 

14.1.2 The Anatomy of the Ear 

Figure 1 is a simplified diagram showing the 
structure of the ear and the terms used in its descrip- 


tion. Three general regions are distinguished: the 
outer, middle, and inner ears. 

The outer ear is open to the air, and the pinna ( P ) 
and external canal ( E ) form a sort of horn for collect- 
ing sound energy. 

The middle ear is also filled with air, obtained 
through the Eustachian tube ( T ) that connects it 
with the throat. 

The inner ear is filled with liquid and contains the 
nerve endings, the stimulation of which by the vi- 
brations of the liquid produces the sensation of 
hearing. 



Figure 1. Structure of the ear. The parts shown are: 
in the outer ear, the pinna (P) and the external canal 
( E ); in the middle ear, the eardrum (D), the ossicles 
(0), and the oval window (IF) and the round window 
(R); in the inner ear, the cochlea ( C ) with the basilar 
membrane (B); the semicircular canals (S) are also 
shown. 

The principal physical problem that is solved by 
the structure of the ear is that of transmitting the 
airborne sound into the liquid of the inner ear. This 
cannot be done directly, since an air-liquid surface 
is a very good reflector of sound. Only a small frac- 
tion of the incident airborne energy would be trans- 
mitted into the liquid. The function of the middle 
ear is to provide an efficient transmitting mechanism. 

The middle ear is separated from the outer by the 
eardrum ( D ) which is a membrane that vibrates in 
response to airborne sound. Three small bones are 
contained in the middle ear. They are called ossicles, 
shown at 0, and are in contact with each other. One 
of them is also in contact with the eardrum, and one 
with a membrane, the oval window (IF) that separates 
the middle ear from the fluid in the inner ear. The 


255 


256 


HEARING AND RECOGNITION 


ossicles form a lever system that efficiently transmits 
vibrations from the air to the fluid of the inner ear; 
they are analogous to impedance-matching trans- 
formers in electrical systems. 

The inner ear itself consists of two major parts: 
the cochlea (C) and the semicircular canals ( S ). The 
latter are primarily a stabilizing mechanism, enabling 
the brain to transmit the necessary nerve impulses 
to keep the body in equilibrium. These canals have 
little or nothing to do with hearing. 

The cochlea, on the other hand, has a major part 
in the hearing process. It is a spiral tube, about 30 
mm long, divided into two galleries by a longitudinal 
membrane — the basilar membrane (B) which is a 
sort of carpet of nerve endings. One of the two gal- 
leries is terminated by the oval window (W) men- 
tioned above, and the other by the round window (R ) . 
As the ossicles press in on the oval window, the fluid 
presses down on the basilar membrane, which in turn 
causes the fluid in the other gallery to press out on 
the round window. 

14 . 1.3 A Theory of Hearing 

The nerve endings of the basilar membrane are 
transverse fibers that vary systematically in length. 
The short fibers located near the oval window re- 
spond to sound waves of higher frequencies; the 
longer fibers at the other end, to those of low fre- 
quencies. That is, the position of the point of maximum 
stimulation depends on the frequency of the tone. a 

In response to a complex sound, the basilar mem- 
brane vibrates with a certain pattern, perhaps having 
several maxima, depending on the frequency com- 
ponents in the stimulus. The auditory nerve endings 
are distributed along the basilar membrane in such a 
way that they can transmit this pattern to the brain, 
which interprets it in terms of the pitch, loudness, 
and quality of the sound. The location of the vibra- 
tion pattern on the basilar membrane determines the 
pitch sensation, while loudness is associated with the 
magnitud e of the vibration. 

a The structure of the basilar membrane suggests that the 
cochlea might be considered as an instrument containing a 
series of resonators, which can be excited by vibrations of 
appropriate frequency; the nerves corresponding to the in- 
dividual resonators then transmit the reaction to the brain. 
This theory was proposed by Helmholtz. There are serious 
defects in the theory: there is a large damping resulting from 
the fact that adjacent fibers are closely coupled and are em- 
bedded in liquid; and the small differences in length and the 
small number of vibrators seem inadequate to cover the wide 
range of 10 or 11 octaves. 


FREQUENCY, CPS 


800 4000 



DISTANCE ALONG BASILAR MEMBRANE 
MM FROM OVAL WINDOW 


Figure 2. Hypothetical stimulus patterns on the 
basilar membrane for several different stimuli. Curve 
A represents the stimulation by a pure tone of low fre- 
quency and low level; curve B a tone of the same fre- 
quency at high level. The stimulation pattern increases 
in both amplitude and extent for greater sound in- 
tensity. Curve C represents a high frequency tone of 
low intensity, curve D one of higher intensity. Curve 
E represents the pattern resulting from a sound having 
a continuous spectrum. The area under any of the 
curves is associated with the loudness of the sound. 1 

Some hypothetical stimulus patterns 1 on the basilar 
membrane representative of several different stimuli 
are shown in Figure 2. Curve A represents the stimu- 
lation produced by a single frequency (pure tone) at 
a low frequency and low intensity level. Curve B 
shows a high intensity level at the same frequency. 
It is apparent that the stimulation pattern increases 
in both amplitude and extent for greater sound in- 
tensity. The broadening of the pattern toward the 
high frequencies is significant and indicates that the 
ear is a nonlinear sound receiver. Curve C represents 
a high-frequency tone of low intensity, Curve D one 
of higher intensity. Curve E represents the pattern 
resulting from a sound having a continuous spec- 
trum, such as ambient water noise. The area under 
any given curve is associated with the loudness of 
the sound. 

The relation between the perceived loudness of a 
sound and the magnitude of the stimulus on the 
basilar membrane is explained as follows: the au- 
ditory nerve contains about 3,000 nerve fibers which, 
analogous to a telephone cable, connect the cochlea 
to the brain. Each nerve fiber responds according to 
the “all-or-none” law, that is, when it is stimulated 
sufficiently to respond at all, it responds at full 



THE HUMAN EAR 


257 


strength. The response of a nerve fiber is analogous 
to the discharge of a condenser. The strength of the 
discharge is independent of the intensity of the sound, 
but the number pf discharges per second does depend 
on the magnitude of the stimulus in the following 
manner. 

The discharge of a given nerve fiber is followed by 
a “refractory period’’ during which the nerve cannot 
react. This period is about 0.001 sec; thus no single 
nerve fiber can respond at a rate greater than about 

1,000 times per second. The refractory period is fol- 
lowed by a “relative refractory period” of about 
0.003 sec during which the nerve gradually recovers 
its sensitivity. Thus a very weak tone of, say, 1,000 c 
may cause a given nerve fiber to discharge no more 
rapidly than about 300 times per second, while in 
the case of an intense tone of that frequency the 
nerve may respond up to 900 times per second. The 
number of responses of a given nerve fiber depends 
on the strength of the stimulus ; moreover, the num- 
ber of nerve fibers excited increases with the intensity 
of the stimulus because (1) a greater area of the 
basilar membrane is activated and thus the stimulus 
pattern on the membrane takes in nerve endings over 
a wider area ; and (2) the high intensity excites nerve 
fibers having higher normal thresholds of stimula- 
tion. It seems reasonable, therefore, to correlate the 
sensation of loudness with the total number of nerve 
impulses arriving at the brain. 

That the periodicity of the stimulus is retained in 
the nerve current reaching the brain is demonstrated 
by the ability of individuals to localize binaurally 
the direction of a pure tone because of the phase 
difference at the two ears. This phenomenon does 
not require each nerve to discharge on every cycle of 
the tonal stimulus but may be the result of certain 
nerve fibers, discharging every other cycle, while 
others may discharge every third or fourth cycle. It 
is only necessary to assume that each nerve fiber 
discharges at the same phase of the vibration of the 
basilar membrane. This mechanism also may com- 
plement the vibration pattern in bringing about 
pitch perception. 


14.1.4 Numerical Data Concerning 
the Human Ear 

This theory suggests how the structure of the ear 
enables it to respond to frequency and intensity 
characteristics of a sound. It is a theory which has 


SIGNAL DURATION. SECONDS 



Figure 3. Graphs of the threshold of frequency dis- 
crimination for several frequencies as a function of 
signal duration . 3 


not been verified in all details and is subject to re- 
vision. The following facts are independent of the 
correctness of the theory outlined above. 

Frequencies from 20 to 20,000 c can be heard by a 
normal, young ear. A change in frequency of less 
than one-half of 1 per cent results in a perceptible 
change in the pitch of a pure tone. This is true for 
long continued tones of frequencies from 500 to 

10.000 c and only if the listening level is comfortably 
loud. 2 If the tone signal has a short duration, the 
ability to hear pitch changes decreases. This is shown 
in Figure 3, where the least perceptible frequency 
change is plotted against the signal duration. It is 
interesting to note that at 1,024 c, the length of the 
signal affects pitch discrimination only if the signal 
length is less than 0.1 sec. 3 This fact is important in 
doppler discrimination in echo ranging. 

The ear is most sensitive at frequencies between 

1.000 and 5,000 cycles, where a sound of approx- 
imately 10 -16 watt/cm 2 intensity can be heard. 
Sound of approximately 10 -4 watt /cm 2 intensity 
produces a sensation of pain rather than of hearing. 
Thus the ear has a dynamic range of about 120 db 
at frequencies around 1,000 cycles. 

A rapid change of 1 db, or slightly less, in the level 
of a pure tone can ordinarily be perceived at all 
frequencies between 50 and 10,000 c if the listening 
level is comfortably loud. 4 

The ability to detect changes in level will be less 
for randomly fluctuating sounds such as noise, than 
for pure tones. However, a simple rhythmic varia- 
tion is very easily perceived, particularly if it is cyclic 
at the rate of about 3 per sec. 

The ear requires approximately 0.2 sec for the 


258 


HEARING AND RECOGNITION 


sensation of loudness to catch up with a sudden 
increase 5 - 6 or decrease of sound level. These dynamic 
properties seem to be determined by neural rather 
than mechanical processes. They influence the re- 
sponse of the ear to tones of short duration such as 
are used in echo ranging. 

Sounds producing the same sensations of pitch and 
loudness still produce different sensations if their 
spectra are different. The general term “quality” is 
used to describe the difference in the complex sensa- 
tions they stimulate. These differences may be suf- 
ficient to influence the masking of one sound by 
another. Since masking is a primary factor in pre- 
venting the detection of signals, its general principles 
will be discussed in greater detail than has been 
accorded to the other aspects of hearing. 

14 . 1.5 The Threshold of Hearing 

Imagine the following experiment. A microphone 
is placed near a sound source which produces a pure 
tone of controllable intensity. Apart from this sound, 
the experimental location is to be very quiet. The 
microphone will convert the mechanical energy of 
the sound to electric energy which can be used to 
operate some device, say an oscilloscope. 

Beginning with a sound intensity of moderate value, 
the intensity of the tone is gradually reduced. It will 
be found that the oscilloscope will fail to operate 
properly before the sound intensity has reached zero. 
This minimum intensity to which the oscilloscope 
will respond depends on two factors. One is the 
amount of energy dissipated in the various parts of 
the microphone; the other is the self-noise of the 
oscilloscope, the microphone, and the circuit. The 
oscilloscope will not operate properly unless the sig- 
nal is at least as intense as the self-noise. The minimum 
sound level that will cause the device to operate 
properly is its threshold, a concept that has been 
discussed earlier in this book. 

Suppose that the receiver is now replaced by a 
human ear, and the same procedure followed. A 
precisely analogous situation results, and for much 
the same reasons. The ear receives the sound energy 
incident on it, is stimulated mechanically, and the 
mechanical energy then is converted to some form 
of nerve energy which activates the brain. Some of 
the incident energy is dissipated in this process. Cor- 
responding to the self-noise of the receiver, there are 
sounds generated by breathing and by the circulation 


of the blood. Thus there is a minimum level which 
must be exceeded by a sound before it can be heard. 
This threshold of hearing corresponds to the threshold 
of the microphone-oscilloscope system. 

The value of the threshold of hearing differs from 
person to person. We say that their acuity is different. 
The average value of the threshold of hearing also 
depends on the frequency. At 64 c it is 0.12 dyne/cm 2 ; 
it decreases more or less uniformly with increasing 
frequency up to about 2,000 c, at which frequency 
it is 0.00041 dyne/cm 2 . This corresponds to the low T - 
est limit of sensitivity mentioned in Section 14.1.4. 
Above 5,000 c it increases with frequency until at 
18,000 c it is 4.1 dynes/cm 2 . 

14 . 1.6 Masking 

Common experience shows that under all ordinary 
circumstances, we hear many sounds at once but are 
usually able to concentrate on the wanted sounds 
and ignore the unwanted background. This back- 
ground is always present; as remarked above, even 
in a very quiet place the self-noise produced by the 
normal internal processes of the human body be- 
comes audible. Thus there is complete analogy be- 
tween the ear and an electronic receiver of sound. It 
will be seen that this analogy is close enough so that 
it is often possible to use the word “receiver” so as 
to include reference to the ear as well as to electronic 
devices. 

While one can ignore the unwanted sounds to a 
considerable extent, their presence does interfere 
with the ear’s ability to detect another sound. This 
effect is technically called masking ; it can be de- 
scribed as the increase of threshold level caused by 
the unwanted sound, and has already been discussed 
in Chapters 9 and 10. 

The laws governing masking are most easily under- 
stood if several cases are distinguished, the classifica- 
tion depending on whether the wanted or unwanted 
sound is a pure tone or a complex one. These will be 
discussed in detail in Section 14.2, but various 
generalities remain to be mentioned in preparation 
for that discussion. 

14.1.7 Psychological Characteristics 
of Sound 

How does the ear distinguish between a specific 
sound and all the other sounds that form a back- 


THE HUMAN EAR 


259 


ground for it? One’s own experience suggests the 
answer. A bosun shouting orders may rely chiefly on 
his ability to produce sounds of an intensity great 
enough to override the clamor of winches, etc. How- 
ever, a shrill whistle will produce a sound that will 
be audible, even though the intensity of the back- 
ground is incomparably greater than that of the 
whistle. In this case the perception is due partly to 
the pitch difference between the signal and the 
background noise, and partly to a decided difference 
in the quality of the two sounds. Again, a rhythmic 
drum beat is audible over many noises; before the 
days of telephone and radio the common method of 
transmitting orders to masses of troops was to use 
drum beats of various rhythmic patterns ; bugle calls 
with very decided rhythm utilized the advantages of 
all the factors mentioned. 

To sum up, the sensations produced by sound 
have at least four distinctive characteristics: 15 (1) 
loudness, (2) pitch, (3) quality, and (4) time pattern. 
In recognizing a particular sound, it is probable that 
all four of these characteristics contribute to differen- 
tiate it from others heard simultaneously. In experi- 
ments, however, the effect of each characteristic can 
be isolated. 

Loudness, pitch, and quality are psychological, 
rather than purely physical, terms. That is, they 
directly characterize the sensation and only indi- 
rectly the sound. It is customary to say loosely that 
loudness is determined by the level of a sound, pitch 
by its dominant frequency, and quality by the spec- 
trum. This explanation is oversimplified. A more 
careful examination discovers that in determining 
any one of the three, all the physical characteristics 
of the sound play a part. Loudness, it is true, is 
primarily determined by the level of the sound, but 
it is influenced also by the frequency and spectrum. 
It has been demonstrated experimentally that a 
moderately high frequency is perceived as being 
louder than a low frequency of the same intensity. 
This is almost implicit in the discussion of the thresh- 
old of hearing given above. If the frequency exceeds 
12 or 14 kc, the reverse is true, and supersonic sound 
of any level is inaudible. Pitch, in its turn, is deter- 
mined largely by the dominant frequency of the 
sound waves, but is influenced also by the level and 
the other characteristics of the spectrum. Quality is 
principally a matter of spectral distribution, and the 

b Other descriptive terms used by musicians, such as timbre, 
and clarity, could also be considered, but are of less impor- 
tance for the present purpose. 


time pattern may consist of systematic changes in 
any of the other three psychological characteristics. 

One point is worthy of particular emphasis. Ignor- 
ing the fact that intensity is not the only factor that 
determines loudness, we may inquire as to the 
mathematical relation between the two. It appears 
that this is not a simple proportionality: that is, 
when one sound is said, by most people, to be “twice 
as loud” as another, the intensity of the one is not 
twice the intensity of the other. In general, loudness 
is more nearly proportional to the level of the sound 
in db above 0.0002 dyne/cm 2 . A just-perceptible in- 
crease of loudness usually accompanies a sudden 
increase of 1 db in sound level, whether the original 
level was 5 or 50 db. 

Binaural and Similar Effects 

A final characteristic that can be used in differ- 
entiating between sounds is their direction of arrival. 
In simple cases, this coincides with the direction of 
the source from the listener. The ability of a human 
being to determine the direction of travel of a sound 
wave depends on the fact that he has two ears, and 
the adjective binaural is frequently used. The judg- 
ment of direction apparently depends largely on the 
difference in loudness as perceived via the two ears. 
Difference in the arrival time of the sound waves 
also contributes to the effect, but appears to be less 
important; this second mechanism is similar in 
principle to the split transducer used with bearing 
deviation indicators [BDI]. 

The current underwater-listening systems make 
little use of the ability of the listener to determine 
the direction of a sound. A few experiments have 
been performed in which the two halves of a split 
transducer were connected (without phase-lag cir- 
cuits) separately to the two earphones of a headset, 
as shown in Figure 4. 

The sensation of a listener as the source moves 
across the axis of the projector is very vivid. The 
source of sound appears to move rapidly along a line 
some distance ahead, until it is about to change from 
left to right, or vice versa. At this moment, when the 
actual source is presumably on the axis of the pro- 
jector, the apparent source suddenly seems to be 
overhead, or even inside the listener’s head. There 
is no doubt that the listener can, in this way, func- 
tion very effectively as a BDI. An apparent motion 
of 180 degrees corresponds to about 6 degrees of 
actual motion. Whether the masking of a signal 


260 


HEARING AND RECOGNITION 


by background is reduced correspondingly, is not 
known. 

In these experiments, the underwater sound was 
supersonic, so that the directivity of the transducer 
was great, and it was made audible by heterodyning. 
Similar effects have been obtained with sonic fre- 
quencies and arrays of hydrophones spaced on the 
hull of the ship, at separations comparable to or 
greater than the sonic wavelengths. During World 
War I, similar arrays of geophones were used to 
detect and locate tunneling operations during trench 
warfare. 


14 2 THE PRINCIPLES OF 

AUDITORY MASKING 


14.2.1 The Masked Threshold 

The level at which a particular sound becomes 
audible differs from the threshold of hearing by an 
amount depending on the extent to which the back- 
ground noise masks the signal. As defined above 
(Chapter 9), this level is the masked threshold ; it is 
the level of the signal when it is audible above a 
particular background noise, 50 per cent of the time. 
This term therefore applies to the signal-noise pair, 
not to the signal alone, although it is measured by 
the level of the signal alone. The value of the masked 
threshold is, however, determined by the level of the 
noise. Raising the level of the noise raises the masked 
threshold of the signal. 

The variable acuity of a listener introduces the 
need for the phrase “50 per cent of the time”; not 
only does the threshold of a signal under identical 
conditions vary from individual to individual, but 
the same individual will sometimes hear a signal and 
sometimes not, even though the level of signal and 
masking noise are the same on the various occasions. 
Thus, a statement of the probability of recognition 
of a signal is required to fix a definite value for the 
threshold level. 

This has already been mentioned in earlier chap- 
ters, but as greater detail now is needed, it may be 
further clarified by describing a typical experiment 
designed to measure the masked threshold. Arrange- 
ments are made so that a number of listeners will 
hear the background noise at a constant and known 
level. Other arrangements are made for producing 
the signal at various levels, and various times. Care 



Figure 4. Schematic of circuit of split transducer, the 
two halves of which are connected (without phase lag 
circuits) separately to the two earphones of a head set. 
This has been used in some experiments in connection 
with the binaural effect in listening to underwater sound. 

is taken so that the listeners cannot determine when 
or at what level the signal is produced except by 
hearing it; they receive no cues from the person 
administering the test, nor from each other. The 


Table 1 . Probability of the recognition of a signal in 
presence of a noise background (background level, 12 db). 


Signal 

level 

(db) 

Vote 

Recognition 

probability 

(%) 

Yes 

No 

10 


50 

0 

11 


50 

0 

12 

2 

48 

4 

13 

9 

41 

18 

14 

16 

34 

32 

15 

32 

18 

64 

16 

43 

7 

86 

17 

49 

1 

98 

18 

50 


100 

19 

50 


100 

20 

50 


100 



THE PRINCIPLES OF AUDITORY MASKING 


261 


o 

o 


SIGNAL LEVEL, DB 


17 18 19 


0 






/ 




0 






/ 




0 





/ 





o 




J. 


BACKGROUND 

NOISE LEVEL= 

12 DB 

o 

0 







Figure 5. Probability of recognition of a pure tone in 
a background of a noise at a constant level 12 db. 
Illustrates Table 1. 


administrator records the level of the signal, and, 
after a suitable interval, instructs the listeners each 
to vote yes or no according as they heard or did not 
hear the signal. 

A typical table of data from such an experiment 
with ten listeners is given in Table 1. Each level of 
the signal was presented five times, so that the total 
number of votes for each level is 50. The recognition 
probability is the percentage of yes votes for a given 
level. This is plotted as a function of signal level in 
Figure 5. 

It is seen that there is no abrupt transition from 
inaudibility to audibility. Instead, the probability of 
hearing the signal increases gradually from zero to 
100 per cent over a 5-db range of levels. This is a 
complication that was not considered in discussing 
threshold levels in the preceding pages. Fundamen- 
tally, there is no one level at which the signal is “just 
audible.” To avoid confusion, threshold levels are 
usually defined as the level at which the recognition 
probability is 50 per cent, but when necessa^ other 
percentages may be used provided they are speci- 
fically indicated. From Figure 5, it is seen that in the 
example, the 50 per cent masked threshold is 14.5 db, 
the 90 per cent threshold is 16.4 db, and the 10 per 
cent threshold is 12.6 db. 

This, also, has already been used in the earlier 
discussion of echo ranging, as has the recognition 
differential. This is the difference between the thresh- 
old level of the signal and the level of the background. 
In the example, the recognition differential for 50 
per cent recognition is thus 14.5 — 12.0 = 2.5 db. 

Two variants of the above experimental procedure 
are in common use. In the first, the level of the signal 
is increased after each presentation, until 100 per 
cent recognition is definitely attained. Thereafter, 
the experiment may be started over at a low-signal 


level, or the level may be successively decreased after 
each presentation. This is called the method of min- 
imal changes. In the second method, the levels 
are changed in a haphazard manner; this is 
the method of random presentation. Each has its 
advantage. 


14.2.2 The Theory of Masking 

The theory of hearing presented above can be 
applied to the masking problem. A given sound 
activates a particular area of the basilar membrane. 
This causes a certain fraction of the auditory nerve 
fibers to be stimulated. The number of discharges 
per second of these nerve fibers depends on the in- 
tensity of the sound. Suppose that while this sound 
is incident on the ear, a second sound is received and 
stimulates the same area. Two effects may occur. 
(1) Additional nerves may be stimulated and their 
discharges added to the number occurring previously; 
or (2) the nerves which already have been stimulated 
may be caused to discharge more rapidly. The effect 
of the second sound will thus be only to change 
the stimulation of an already stimulated area. 
Unless the change is great enough, it will not be 
perceived. 

If the second sound has a markedly different 
spectrum than the first, it may stimulate a different 
area of the basilar membrane, and the second sound 
may be perceived just as though the first were absent. 

It appears from these considerations that the 
masking of one sound by another depends on the 
areas of the basilar membrane which are stimulated, 
and hence on the spectral character of the two sounds, 
as well as on their intensity. In the following pages 
a resume will be submitted of the experimental re- 
sults observed in experiments on masking of (1) one 
pure tone by another pure tone; (2) a pure tone by 
background noise having a continuous spectrum; 
and (3) a complex sound by a second complex 
sound. 


14 . 2.3 The Masking of One Pure Tone 
by a Second Pure Tone 

Experiments on the masking of one pure tone by 
another pure tone have already been discussed in 
Chapter 9. The results will be summarized here for 
completeness. 


262 


HEARING AND RECOGNITION 


40 


50 


FREQUENCY, 

500 


CPS 

1,000 


30 


I 

s 

-I 


10 


2,000 


5,000 


10,000 

110,000 


MASKED THRESHOLD LEVEL OF SINGLE 
FREQUENCY TONE (FLETCHER) 

o CRITICAL BAND WIDTHS FROM DIRECT 
MEASURMENTS (FLETCHER) 




1.000 


Figure 6. Masked threshold level of single-frequency tone and critical bandwidths from direct measurements. 18 


1. Masking is greatest at frequencies in the vicinity 
of the masking tone; in the presence of a 1,300-c 
masking tone of 60-db c level, the masked threshold 
of a tone of 1,250 c is raised 46 db above the thresh- 
old of hearing, whereas the masked threshold of a 
tone of 3,000 c is raised only 8 db. 7 

However, when the frequencies of the two tones 
are very close together, the resulting beats enable 
the listener to hear the masked tone more easily, 
and the masking is reduced to some extent. In the 
example cited above, the masking in the immediate 
neighborhood of 1,200 c is nearly 10 db lower than 
that at 1,150 or 1,250 c. 

2. Masking is not reciprocal ; that is to say, a 60-db 
masking tone of 1,250 c will not necessarily raise the 
threshold ol a 1,300-c sound 46 db. In general, the 
masked thresholds are higher on the high-frequency 
side of a pure tone; for example, a 1,200-c tone of 60- 
db level will raise the threshold of a 1,400-c tone 
36 db, but that of a 1,000-c tone only 30 db. More- 
over, it is found that the harmonics of the masking 
tone have a masking effect. 

3. The increase in the masked threshold is roughly 
the same as the increase in the level of the masking 
tone. Thus, a 1,200-c masking tone of 80 db will 
mask a 1,250-c tone about 66 db, compared with the 
46-db masking of the 60-db tone mentioned in para- 
graph 1. For very low and very loud tones, this 
simple relation is no longer true. 

c Here and elsewhere in this chapter the levels of airborne 
sounds are specified in db above 0.0002 dyne/cm 2 (see Chap- 
ter 1, Figure 1). 


14.2.4 The Masking of a Pure Tone 
by Complex Sound 

Most masking noises encountered in practice are 
complex, and have their power distributed over a 
wide band of frequencies. Correspondingly, they 
stimulate a larger area of the membrane, although 
the stimulus at any point will be weaker, than in the 
case of a pure tone of the same level. 

Since the masking effect of a pure tone is largely 
confined to a relatively narrow band of frequencies, 
we may expect that, conversely, a pure tone will be 
masked only by those components of a complex 
sound whose frequencies are adjacent to that of the 
sound being masked. That is to say, there should be 
a more or less definite critical bandwidth w(f) such 
that any components of the noise beyond w(J) do 
not raise the masked threshold. This critical band- 
width should be the same (or nearly so) as that 
already discussed in Chapter 9. The masking effect 
of a complex sound at each frequency will thus be 
determined by the power level in the critical band 
involved. Call this C(f); it is related to the spectrum 
level of the noise N(f) by the relation 

C(f)=N(f) + 10 log w(f). 

The quantity C (/) is called the critical band spectrum 
level. 

If this hypothesis is correct, the threshold of a pure 
tone of frequency /, when masked d by a complex 

d This ignores the increased masking when the levels are 
unduly high. 


THE PRINCIPLES OF AUDITORY MASKING 


263 


FREQUENCY, KC 



Figure 7. Experimental data on critical band levels, 
using two observers. The solid curve is plotted from 
the data in Figure 6. 


sound, should be just equal to C(f). The verification 
of this theory by experiment is shown in Figure 6. 1 - 8 
If L(f ) is the masked threshold level of a pure tone 
of frequency /, it is expected that L(f) = C(f) or, in 
other words, that 

L(f)-N(f) = 10 log w(f). 

The masking was by thermal noise, which had a 
spectrum level N(f) that was the same for all fre- 
quencies. The signals were pure tones, for which 
threshold levels were determined experimentally as 
described above and plotted as circles. The values of 
L(f) —N(f) calculated in this way are shown by the 
open circles and the left-hand scale. The values of 
w(f) were determined by experiments on the masking 
of one pure tone by another. The agreement between 
theory and experiment is very satisfactory. 

Figure 7 shows the agreement between theory and 
experiment in another case. The curve is the graph 
of C(/), the critical band spectrum of the masking 
noise, while the points are the masked thresholds 
L(f ) of pure tones, as determined by two listeners. It 
should be clearly noted that, while C(f) and L(/) are 
equal, the two numbers are determined by different 
experimental and computational procedures. 

The recognition differential for this case is still 
defined as the masked threshold level of the pure 
tone minus the overall level of the noise. However, 
the overall level of the noise depends on its whole 
spectrum, while the masking effect is determined 
only by the spectrum in the immediate critical band 
of the pure tone signal. Consequently, the laws of 
masking cannot be easily formulated in terms of 


recognition differentials. The latter are useful in 
many cases, but when either or both of the sounds 
are not pure tones, the critical band spectrum yields 
more information and should be used whenever 
possible. 

14.2.5 The Masking of One Complex 
Sound by Another Complex Sound 

The success of the critical band theory in predict- 
ing the masked thresholds of pure tones leads one to 
anticipate that it will be equally successful in pre- 
dicting the masking of one complex sound by another. 

Let C,(J) and C n (f) be the critical band spectra 
of the signal and masking noise, respectively. It has 
been found that if C s (f) is greater than C„(/) for some 
frequency /i, then the sudden starting or stopping of 
the signal can be heard at least 50 per cent of the 
time. If C,(f ) is less than C n (f ) for all frequencies, 
the signal will be heard less than 50 per cent of the 
time. 

These relationships are shown schematically in 
Figure 8. The three parts of the figure show the same 
signal and noise, the level of the signal being low in 
A and high in C. 

Several other interesting conclusions can be reached 
from a study of these figures. Thus, Figure 8B shows 
that, as the signal level is increased, it will first 
become audible as a sound of pitch f T . This is called 
the threshold frequency. Figure 8C shows that at 
higher level many (though not all) frequency com- 
ponents are audible. The audible components of the 
signal are indicated by shading. The components 
between /i and/ 2 remain inaudible even at this higher 
level. This theory has been fairly well confirmed by 
experiment. 9 

As in the case of the masking of a pure tone by a 
complex sound, the laws are not easily formulated in 
terms of the recognition differential. The latter is 
sometimes a useful practical concept, but its use may 
lead to mistakes unless the critical band spectra are 
available as supplementary information. 

14.2.6 Adjacent Masking 

In using the critical band spectrum criterion, it is 
necessary that the masking noise have a continuous 
spectrum or at least that single-frequency compo- 


264 


HEARING AND RECOGNITION 


CRITICAL BAND SPECTRA 

FREQUENCY 




Figure 8. Schematic diagrams illustrating recognition 
of complex signals against a complex noise background. 
The three parts of the figure show the same signal and 
noise spectra, the signal spectra being shown at differ- 
ent levels. 

nents do not have too high a level. Very strong pure 
tones mask a much wider region on the basilar 
membrane than their critical band spectra indicate; 
there occurs a “spilling over” of masking onto fre- 
quencies adjacent to the ones at which the energy is 
located. This effect is called adjacent masking. It fol- 
lows that if components outside the critical band of 
a particular tone under consideration contribute ap- 
preciably to the masking in the band itself, a greater 
sound level will be required for the tone to reach the 
masked threshold. 





Figure 9. Diagram illustrating the effect of the re- 
ceiver in detecting underwater sound signals. (A) The 
spectra of the underwater signal and sound. (B) The 
response curves of two receivers. (C) The signal and 
noise spectra at the output of the receiver systems. 

From the shape of the stimulation patterns on the 
basilar membrane it is apparent that a very loud 
sound will stimulate several critical bands on either 
side of its own. It may happen that, in the critical 
band centered at frequency/, the stimulation due to 
the noise components of this frequency is weaker 
than the stimulation due to unusually strong com- 
ponents of considerably lower or higher frequency. 
It is only when this is the case that adjacent 
masking becomes significant; and it is with this 
qualification that the term is used to designate 
the effect. 



THE PRINCIPLES OF AUDITORY MASKING 


265 


14.2.7 Variable Levels 

The preceding discussion of masking applies to 
sounds that have a constant loudness and quality. 
Ship sounds are usually not constant, but may have 
a variable overall level, or a variable spectrum, or 
both. For example, the main engine and gear train 
driving the screws may contribute a sound of con- 
stant level and spectrum. The screw itself may con- 
tribute a sound of different spectrum, the level of 
which changes as the screw turns. The resultant is a 
sound for which level and spectrum both change 
periodically. 

In such cases, it is reasonable to suppose that the 
highest values of C s attained during the changes will 
be the important ones in determining recognition. In 
addition, the changes, particularly if they are rhyth- 
mic, may “call attention” to the presence of the 
signal. 

The quantitative laws governing this increased 
audibility of rhythmic sounds have not been carefully 
worked out, but the existence of the effect is certain. 
It must be considered in any application of the 
foregoing principles. 


14.2.8 Influence of the Receiver on the 
Audibility of Underwater Sound 

In this chapter, the discussion has been entirely 
concerned with airborne sound levels and spectra; 
that is, with the sound output of listening gear. In 
most other parts of this book, the discussion has 
dealt with the underwater sound levels and spectra. 
Since the receiver amplifies the sound and may 
modify its spectrum, it may have an effect on the 
recognition of signals. 

To see this, two receivers may be compared (Fig- 
ure 9). The graphs A show the critical band spectra 
of the underwater signal and noise. Graphs B are 
the response curves of two receivers, and curves C 
are the sound outputs of the two receivers, deter- 
mined by combining graphs A and B as discussed in 
Section 14.2.5. 

For receiver No. 1, the signal will be clearly 
audible, but for receiver No. 2, the signal will be 
inaudible. This is perhaps an extreme case, but 
serves to illustrate the manner in which the response 
curve of a receiver can influence the audibility of a 
signal. 


Chapter 15 

SONIC AND SUPERSONIC LISTENING 


15 i THE MAXIMUM RANGE EQUATIONS 

i5.i.i Two Specifications for 

Listening Receivers 

I n section 9.1.7, two general specifications for 
echo-ranging receiver amplifiers were given. The 
purpose of these specifications was to prevent the 
limitation of echo ranges by factors under the con- 
trol of the electronics designer, and to insure that 
only those limitations inherent in the sea need be 
considered in this book. Similar specifications for 
listening receiver amplifiers can be written, but they 
are somewhat more complex. 

This increased complexity results from the need 
for wider pass bands in listening than in echo-rang- 
ing receivers. This is especially true of sonic listening 
gear. Even in the discussion of echo-ranging receivers, 
the concept of spectrum level was used, but it was 
only necessary to consider a single frequency. This 
was because the spectrum levels could be considered 
as approximately constant over the whole range of 
frequencies within the pass band of the receiver. 

In order to simplify a fairly complicated discus- 
sion, it is well to begin with the second specification 
of Section 9.1.7, and to reformulate it as a definition. 

The listening band of a receiver-hydrophone system 
is that range of frequencies over which the inherent 
noise is so low that it is possible to hear water noise, 
if the loudspeaker is in a quiet place. More precisely, 
if the inherent noise spectrum is recalculated in terms 
of the spectrum of an equivalent noise in the water, 
the listening band is the range of frequencies for 
which this equivalent spectrum is below the actual 
water-noise spectrum. In this discussion, the critical 
band spectrum level is to be used, rather than the 
1-c spectrum level, although often the conclusions 
will not be much affected if the 1-c spectrum level is 
used. An exception occurs if there are many single- 
frequency sounds (such as overtones of the 60-c 
ship's power) in the self-noise. In principle also, such 
single-frequency tones may introduce gaps in the 
listening band; for this and other reasons, they are 
undesirable. 

Two general classes of listening systems can be 
distinguished. The first includes those whose listen- 


ing band falls in the supersonic region, and whose 
output is made audible by a heterodyne change of 
frequency. The other class has its listening band in 
the audio frequencies, and does not need a hetero- 
dyne stage to render its output perceptible. 

The choice of a suitable listening band is obviously 
one of the designer's first problems. It can only be 
determined by a consideration of all possible factors 
affecting listening. 

With the aid of this definition of the listening band, 
the first specification for listening amplifiers can be 
formulated simply: 

Specification 1. The gain of the listening amplifier 
and loudspeaker, and their location on board ship, 
should be such that all frequency components of 
water noise within the listening band can be heard 
despite the sound of nearby activities. 

When this specification is fulfilled, the airborne 
noise will never prevent the detection of a signal. 
The variation in spectrum level over the listening 
band introduces complications that were not present 
in the echo-ranging case. As a possible example, 
consider a listening band extending from 100 to 
10,000 c: over this frequency range the spectrum 
levels of self-noise and water noise may vary by 50 
to 70 db, and that of the wanted signal by at least 
as much. This brings two dangers with it: the intense 
low-frequency components may overload the amplifier 
when its gain is sufficient to give the high-frequency 
components an adequate level ; and if this is not the 
case, the very loud lower frequencies may deafen 
the listener, so that he cannot hear the weaker high 
frequencies. This is the “adjacent masking" discussed 
in the previous chapter. 

These dangers can be avoided if the response of 
the early stages of the amplifier is such that the low 
frequencies are amplified less than the high fre- 
quencies. This brings us to the next specification: 

Specification 2. The overall response curve of the 
system should be such that all frequency components 
of water noise are presented to the listener's ear at 
about the same loudness. 

When these two specifications are complied with, 
the maximum range obtainable with the receiver 
will depend only on the pass band and on conditions 
beyond the control of the electronics designer. A less 
important consequence is that sound levels can be 


266 


THE MAXIMUM RANGE EQUATIONS 


267 


expressed in terms of their underwater equivalents, 
rather than by giving their actual levels at the 
listener's ear. The gain of the receiver thus disap- 
pears from the equations which are given in the fol- 
lowing sections. 

15 . 1.2 The Determination of 

Maximum Ranges 

As in the case of echo ranges, there is no one range 
at which the target suddenly becomes undetectable. 
The maximum listening range must again be defined 
in terms of a given probability of detection, usually 
50 per cent. 

The analysis of the factors influencing the maximum 
range at which a target can be heard over a given 
listening system has the same objectives as the cor- 
responding problem in echo ranging. The designer 
will need the information so that the best system for 
a given purpose can be built. The fleet will need 
more specific predictions, based on prevailing oceano- 
graphic conditions, so that appropriate operational 
decisions can be reached. 

15 . 1.3 General Principles of 

Range Calculation 

The problem of listening differs from the corre- 
sponding echo-ranging problem in that the target is 
not insonified from the listening station, but is itself 
the source of the signal. Consequently, in calculating 
listening ranges, there is no term corresponding to 
the target strength T which occurs in echo-ranging 
calculations. The steps in the listening process are: 

1. The emission of the signal by the target. 

2. The transmission of the signal to the receiver. 

3. The detection of the signal at the listening 
station. 

If the source level of the signal is S, its level L(r), 
at a point r yards distant from the source, is given 
by 

L(r) = S — H(r)j (1) 

where H(r) is the transmission loss in decibels. 

The signal will be detectable only if L(r) is at least 
equal to the level of the background noise, plus the 
recognition differential M. The noise level N will be 
expressed as equivalent isotropic water noise, so that 


the effective level will be N + D where D is the direc- 
tivity index of the hydrophone (see Section 13.3). 
The directivity index is a negative number, so that 
N + D is less than N. The signal will be heard only 
if its level exceeds that of the noise by an amount 
greater than the recognition differential M , 

L'Z N + D + M, (2) 

or, using equation (1), 

S-H(r)^N + D + M, 

whence 

H(r)^S-(N + D + M). (3) 

In order to facilitate discussion of these equations, 
the quantity (N + D + M ) appearing on the right of 
equation (2) is called the recognition level , and 
S— M), the available signal output. The 

actual level S — H{r) must exceed the recognition 
level, and hence the transmission loss must be less 
than the available signal output. 

“Available signal output" is clearly an omnibus 
term and summarizes the effect of a large number of 
factors. The individual terms in equation (3) have 
been discussed quantitatively in the course of the 
preceding chapters of this book. At present, it is 
necessarjr to keep clearly in mind the relation be- 
tween them as given by equation (3) ; for the problem 
of maximum listening ranges can be discussed in- 
telligently only with regard to the manner in which 
these quantities vary from one set of conditions to 
another. 

15.1.4 The Maximum Range Equations 
in Echo Ranging and Listening 

It is instructive to realize, at this point, that each 
of the terms in equation (3) differs decidedly from 
the same term in the corresponding equation in echo 
ranging. The sources in the two operations have 
almost no characteristic in common. In echo ranging 
the signal has a very definite quality and particular 
frequency, and its source level remains reasonably 
constant. In listening, the exact opposite is true: the 
signals are extremely variable and unpredictable; 
they have a wide frequency range and great vari- 
ability of spectral distribution; their source levels 
may vary 100 db or more. The echo-ranging pro- 
jector is highly directional, while sound is emitted 
almost equally in all directions by a ship's hull and 
screws. 


268 


SONIC AND SUPERSONIC LISTENING 


The background noise (other than reverberation) 
which causes the masking of the signal in echo rang- 
ing is comprised in a relatively narrow band of 
supersonic frequencies, and is of a different quality 
from the signal. In listening, it may be more or less 
similar to the signal in frequency distribution and is 
thus likely to be even more serious than in echo 
ranging. On the other hand, in listening there is no 
reverberation to mask the signal; for that reason 
there is also no doppler to assist recognition. In echo 
ranging, the target noise is part of the masking 
background; in listening, it is the signal. 

The directivity index of echo-ranging gear is 
alwaj^s a large negative number of the order of — 20 
or more; in present listening practice, the receiving 
hydrophone is highly directional only for supersonic 
sound. 

The recognition differential in the two operations 
is essentially different. In echo ranging two recogni- 
tion differentials must be considered, one for the 
case when reverberation masks the echo, which 
happens at short ranges, another for the case when 
the echo is masked by noise, as it is at long ranges. 
In listening, the signal is always masked by noise, 
but it should be noted that the conditions affecting 
recognition are different because of the different 
nature of the signal. 

Finally, the transmission of the sound emitted by 
targets in listening differs from that in echo ranging. 
First of all, it is a one-way process in listening and a 
two-way process in echo ranging. This would seem 
to make the transmission loss less important in 
listening, and result in longer ranges. However, this 
is not necessarily the case; the source levels are in 
general lower than in echo ranging. An important 
exception occurs when the target is transmitting 
echo-ranging pings, and the listening system is 
supersonic. In that case, the signals are obviously 
identical. Moreover, when echo ranging on a large 
target, the target strength is a positive quantity and 
partially cancels the additional magnitude of the 
transmission-loss term in the echo-ranging equation. 
Secondly, if the listening system uses sonic fre- 
quencies, the attenuation is much less than that of 
the supersonic sound used in echo ranging. The image 
effect causes additional losses at moderate range in 
the sonic band, which is, on the other hand, some- 
what less affected by thermal gradients. Since the 
sources are nondirectional, sound reflected from the 
bottom is very important in listening. Between them, 


this second group of factors influencing transmission 
loss is largely responsible for the longer ranges at 
which detection by sonic listening is possible. 

i 5 .i 5 Critical Band Spectrum Levels 

As has been discussed in Chapter 14, the various 
frequency components of a wide-band signal have 
different audibility, so that as the signal level in- 
creases, detection usually occurs first at a single 
frequency. As the level increases still further, other 
frequencies become audible. Consequently, equations 
(2) and (3) should be considered as applying to a 
single frequency band; or better still, as typical of a 
large number of equations, one for each frequency 
band. If the levels entering them are based on the 
critical bands of the ear, the recognition differential 
will be zero, and the equations simplify to 

US)>NU)+D[f), (4) 

H(rJ)^S(f)-N(f)-D(f), (5) 

where the notation indicates explicitly that the criti- 
cal band in question centers at the frequency/. Thus 
N(f) and S(f) are the critical band spectra of noise 
and source, respectively, and H(rJ) is the transmis- 
sion loss for this frequency. Those frequency com- 
ponents of the signal for which the mean level is 
higher than the recognition level will be heard; the 
rest will be inaudible most of the time. If the mean 
level of all frequency components is less than their 
recognition levels, the presence of the target will 
probably be undetected. a 

If the range to the target is opened from a very 
short range, the value of the transmission loss H(r,f) 
will, in general, increase for each frequency /. At 
some range it will become equal to the available 
signal output at that frequency; for longer ranges, 
that frequency will be heard less than half the time 
and rapidly become inaudible all of the time. 

The maximum listening range is defined as the 
greatest range at which the transmission loss at one 
or more frequencies is less than the available signal 
output at those frequencies. At this range, the trans- 
mission loss at other frequencies may exceed their 
available signal output. 

a This statement may require slight modification. If the 
critical band spectra of signal and noise are nearly parallel, 
the signal may be heard even when the level of all signal 
components is several db less than the noise components. 
This effect, however, has not yet been definitely established. 


GENERAL APPLICATIONS OF THE MAXIMUM RANGE EQUATIONS 


269 


The application of this definition and of equations 
(4) and (5) encounters practical difficulties in that 
to date most measurements of sound output S and 
noise levels N have been made in wide bands, so 
that the critical band spectra are often not known. 
Some data on the spectrum levels of ship sounds 
have been published, but the experimental methods 
used in their determination have not always been the 
best. The spectrum levels of ambient noise are, per- 
haps, more accurately known, but data on the self- 
noise of surface vessels is incomplete. The lack of 
data should be rectified. In the interim, equations 
(2) and (3) have been used : the levels S and N enter- 
ing them are overall levels, whose values are tabu- 
lated in Chapters 12 and 13. This does not eliminate 
the effects of our ignorance: that makes itself felt as 
ignorance of the proper values of the recognition 
differential M and of the transmission loss H. 

This could only be overcome by guessing. For 
example, the overall transmission loss of a given 
signal depends on its spectrum in a complicated way. 
This difficulty was often eliminated by the simplify- 
ing assumption that the transmission anomaly is 
zero, so that H{r) = 20 log r, but this was a bad guess 
(see Chapter 3) . Similarly, the directivity index var- 
ies with the spectrum; some guess as to its effective 
value had to be made. The same was true of the 
recognition differential. 

Since submarines have made more use of listening 
than have surface vessels, data for the calculations 
have been accumulated. 8 Even here, however, the 
data has been restricted largely to that relevant to 
existing installations. 

The difficulties in using equations (4) and (5) are 
largely those of present ignorance; the difficulties 
inherent in the wide-band calculation are more fun- 
damental. The basic objections to them are less seri- 
ous in the case of supersonic listening, however, since 
in this frequency range all spectra are simple and the 
listening band is relatively narrow. 

is 2 GENERAL APPLICATIONS OF THE 
MAXIMUM RANGE EQUATIONS 

15.2.1 Reduction of Sound Output 
for Defense 

The use of listening by the enemy as a means of 
detection can obviously be countered by reducing 
the sound output of friendly vessels. Such a program 


has been actively pursued in the case of the sub- 
marines of the U. S. Navy. No corresponding program 
has been followed in the case of surface vessels. The 
narrow margin by which the Battle of the Atlantic 
was won, coupled with the probability that future 
submarines will rely even more on listening as a 
means of detection and fire control, indicates that 
serious thought should be given this matter. The in- 
creased use of homing torpedoes operating on listen- 
ing principles is a further reason for such a program. 
The maintenance of radio silence is a recognized 
countermeasure against attack from the air. The 
achievement of underwater silence is more difficult 
but may be essential. 

The ideal objective is to make the signal output 
unavailable to the enemy gear. Since the available 
output is S(J ) — [N(f) + D(f) + M(f)],it involves fac- 
tors that cannot be determined without knowledge 
of the enemy gear. However, it is certain that N can- 
not be made less than the ambient noise level. Some 
estimate of the directivity index D in various fre- 
quency ranges can be made. The recognition differ- 
ential M will be zero for detection by an operator; 
for present homing devices, it is presumably a positive 
number, but the possibility of devices operating 
with negative values of M is not excluded. 

Thus, some estimate can be made of the largest 
value of S(f), the sound output of a ship, which is 
tolerable if the ship is to be completely undetectable 
at that frequency. This may be unachievable, but 
even so, it may be useful to reduce S as much as 
possible. It will be shown that the maximum range 
sometimes depends very critically on the available 
signal output. Thus a relatively small reduction in 
S may make a great difference in the range at which 
the enemy can detect the vessel. 

15.2.2 Reduction of the Noise 

Background 

Most of the sound sources aboard ship which 
radiate to a distant enemy also contribute to the 
self-noise which interferes with use of its own listen- 
ing gear. The quieting of these sources will thus 
contribute in some measure to increasing the signal 
available for the detection of enemy vessels. This is 
obviously the case with the sound from the ship’s 
screws. 

However, not all sources of self-noise radiate sound 
to a distance. This is especially true of circuit noise, 


270 


SONIC AND SUPERSONIC LISTENING 


FREQUENCY, KC 


FREQUENCY, KC 


0.1 0.2 0.3 0.5 1.0 2.0 3.0 5.0 10 




Figure 1 . The calculation of the available signal level: 
self-noise background. 


Figure 2. The calculation of the available signal level 
ambient noise background. 


and electrical pickup. The turbulence and bubbles 
near the hydrophone are probably no great aid to 
enemy listening and may be the most serious source 
of self-noise. 

The elimination of circuit noise is essentially a 
problem for the electronics engineer. That component 
caused by electrical pickup from other equipment 
aboard ship can be reduced by proper design of all 
circuits, and by proper maintenance of commutators 
and other mechanical switches whose operation is 
semicontinuous. The streamlining of hydrophones 
and their proper mounting will further reduce the 
noise background. 

A systematic study of the causes of self-noise will 
undoubtedly result in appreciable improvements over 
existing installations. However, a lower limit to the 
value of N is fixed by the ambient noise of the sea 
itself. The only countermeasure for this is the use of 
directional hydrophones, which lower the value of 
N + D when ambient noise is the major component 
of N. In general, directivity will also discriminate 
against the localized noise sources in the ship’s hull, 
unless the hydrophone happens to be trained toward 
them. 


15.2.3 Choice of Listening Band 

In Section 15.1.1, the listening band was defined 
in terms of the characteristics of the receiver and of 
the noise background. However, these characteristics 
are to some extent under the control of the designer. 
This is obvious in the case of the electronic com- 
ponents of the system; but the control of the noise 
background basically requires the consideration of 
all designers engaged in the construction of the ship, 
beginning with the naval architect. Such a focus of 
attention on the needs of the sound gear has not 
been possible in the past. The recognition of the 
critical nature of submarine warfare in World War 
II may make consideration of control of noise back- 
ground imperative in the future. 

For the present, it may be assumed that the elec- 
tronic components of the amplifier can be constructed 
so as to place the listening band in any frequency 
range desired. It will then be reasonable to use a fre- 
quency range in which the available signal is high. 
This will not necessarily insure the greatest range of 
detection — that will also depend on the transmission 
loss at the different frequencies — but for the moment 



GENERAL APPLICATIONS OF THE MAXIMUM RANGE EQUATIONS 


271 


FREQUENCY, KC 



Figure 3. Available signal levels at various speeds 
(schematic). 


the problem may be simplified by assuming that a 
high available signal is the major desideratum. 

The manner in which the three factors S, N, and 
D influence the available signal output is then illus- 
trated schematically in Figures 1 and 2. The spec- 
trum of the actual sound output of the source is 
schematic but shows machinery peaks in the region 
of 100 to 600 c, and a general drop until cavitation 
noise from the screws becomes dominant between 

3.000 and 10,000 c. The self-noise curve of Figure 1 
is again schematic but shows a steep slope over the 
whole range. As a result, the whole trend of the 
available signal output reverses that of the actual 
source output. The greatest available signal occurs 
at 10,000 c or higher; and it would seem reasonable 
to place the listening band in the supersonic region, 
or at least in the high audible. This figure presumably 
represents the ideas which prevented Great Britain 
and America from exploiting the possibilities of the 
sonic frequencies prior to World War II. 

Figure 2 is based on the same actual sound output, 
but assumes that self-noise has been eliminated, 
leaving ambient noise as the dominant background. 
A moderately directional hydrophone is also pre- 
supposed. The available signal is then no higher at 

10.000 c than is the machinery peak at 600 c. On the 
basis of available signal output, there is thus little to 
choose between the sonic band and the supersonic. 
It has already been seen that the transmission loss 
of the frequencies below 1,000 c is much less than 
that of the supersonic frequencies. Hence the case 
for the sonic frequencies is much more favorable. 
This figure presumably represents the ideas that 
caused Germany to develop sonic listening systems. 

It should be emphasized that these figures are 
quite schematic. It would be inappropriate to at- 


FREQUENCY, KC 



tempt any final decision between sonic and super- 
sonic listening at this time. The question is a very 
complex one and its answer is not known. The pur- 
pose of the foregoing discussion was to indicate the 
type of data and the kind of reasoning that will be 
needed in arriving at the answer. 

15 . 2.4 The Range Prediction Problem 

In order to provide basic data for operational 
decisions, it is desirable that the fleet be supplied 
with summary tables, listing the ranges at which 
detection of various targets can reasonably be ex- 
pected under each of a number of conditions (bathy- 
thermogram, speed of searching vessel, type of gear, 
etc.) . The purpose of the present section is to indicate 
the manner in which such tables can be prepared; 
the graphs presented in the course of the discussion 
are entirely schematic, especially those of Figure 4. 

Again, graphs of available signal level as a function 
of frequency must first be prepared for each type of 
target and a given type of listening gear. The speed 
of the searching vessel will also affect these graphs, 
so that a typical work sheet may contain several 
graphs (see Figure 3). Since the sea state and other 
oceanographic factors, such as snapping shrimp, 
affect the noise background, these must also be con- 
sidered. In principle, a large number of such graphs 
must be prepared, although in practice short cuts 
can be found to reduce the number needed. 

To determine the maximum range, the transmis- 
sion loss H(r,f) is also plotted, as in Figure 4, using 
the same scale as for Figure 3. As the transmission 
loss depends on thermal conditions, etc., several such 
curves must also be prepared. Since transmission loss 



272 


SONIC AND SUPERSONIC LISTENING 


FREQUENCY, KC 



Figure 5. Graphical computation of maximum listen- 
ing ranges (schematic). 


and available signal must be compared, it is con- 
venient to plot all curves on transparent paper so 
that they can be superposed. 

The result of the superposition is shown in Figure 
5, only one curve of available signal level being shown 
to avoid confusion. Since the available signal must 
be greater than the transmission loss, it is seen that 
at 7,500 yd the components of frequency /i to f 2 or 
greater than/ s are audible (always provided they are 
within the listening band of the system). At 10,000 
yd, the transmission loss and available signal curves 
are tangent at / 0 , hence 10,000 yd is the maximum 
range. 

While this method of calculation may seem com- 
plex, the above description is itself only schematic 
and does not mention all the factors that must be 
taken into account. These other factors, such as 
fluctuation, time pattern, etc., can all be considered 
as influencing either the available signal or the 
transmission-loss curves. The method having been 
outlined, the separate factors will next be discussed 
in greater detail. 

15.3 SONIC LISTENING 

15.3.1 The Sound Output 

The sources of the signal in listening are surface 
vessels, submarines, torpedoes, explosions of depth 
charges, and echo-ranging signals of other vessels. 
The main source of the high-frequency sound output 
of ships is the cavitation produced at the screws. 
Cavitation sounds have a comparatively continuous 
spectrum, the level of which falls off about 6 db per 
octave on the average. They are sufficiently uniform 


in character so that it is possible to determine the 
cavitation spectrum of a given class of ship at a given 
speed by taking a single measurement at some fre- 
quency, say 1 kc or 5 kc. Enough measurements on 
cavitation sounds from various sources have been 
made to enable the prediction of their level for any 
class of ship at any speed within about 5 db. 

This is not true of machinery sounds, which are 
the dominant source of low-frequency sound (less 
than 1 kc) at low speeds. These sounds have very 
complex and irregular line spectra, and differ widely 
among different individual ships. They are heard as 
rumbles, squeaks, groans, and whines. 

In order to determine the role played by these 
single-frequency peaks in range prediction, some 
average value must be chosen. Available data show 
examples of these peaks with height in a 1-c band 
ranging from 15 to 40 db above the average spectrum 
level of the ship sounds. The peaks can be allowed 
for statistically by replacing the average spectrum 
by another curve lying above it and indicating the 
average height of the peaks. At frequencies below 
1,000 c, this line of peaks runs above but parallel to 
the average spectrum, but above this frequency it 
rapidly approaches the average because machinery 
sounds are predominantly low frequency. 1 

15.3.2 Directivity in Sonic Listening 

In sonic listening the problem of hydrophone 
directivity is usually discussed in connection with 
the determination of the bearing of the target. How- 
ever, it enters also in the range problem, and it does 
this in two ways. In order for a signal to be detected, 
it is necessary that there be a noticeable change in 
the sound heard. Since changes are constantly oc- 
curring even in the background noise, a gradual 
change due to a signal of increasing level will not be 
noticed so soon as would a sudden change due to a 
signal that is turned on and off. This on-and-off 
feature may be supplied by the listener, if he trains a 
directional hydrophone on and off the target bearing. 
Complete data on the value of this procedure are 
not available, but it is thought to be appreciably 
better than would be mere listening on a single 
bearing. 

In the second place, a directional hydrophone 
discriminates against isotropic ambient noise, the 
amount of discrimination being given by the direc- 
tivity index, as already noted. 


SONIC LISTENING 


273 


FREQUENCY, KC 

0.1 0.2 0.3 0.5 1.0 2.0 3.0 5.0 10 



Figure 6. Directivity indices of various types of hydro- 
phones for sonic frequencies. 


The computed directivity indices of various sonic 
hydrophones are shown in Figure 6 for frequencies 
below 10 kc. At the frequency of 1 kc, the directivity 
index of the 3-ft line and piston hydrophones is only 
— 2 to — 3 db. Compared with these, the directivity 
index of — 10 db and of the 8-ft ring hydrophone is 
outstanding. The structural difficulties of such a 
large hydrophone can be avoided by the use of arrays 
of small hydrophones mounted in fixed positions on the 
hull. The training is accomplished by phase-shifting 
networks. It is estimated that the increased directiv- 
ity may increase ranges by as much as 10,000 yd. 2 

15 . 3.3 Directivity and Bearing 

Determination 

The accurate determination of bearings depends 
very strongly on the directivity of the hydrophone, 
increasing with directivity up to the point where the 
narrowness of the beam makes it difficult to main- 
tain contact with the target. Good directivity in the 
lower frequency range may enable the operator to 
obtain a more-or-less tentative bearing at long range, 
and, as the range is closed, the bearing determination 
can be made with increasing accuracy. 

The simplest way to increase the directivity of a 
given kind of listening gear is to make the hydro- 
phone larger, but the practical limits of size are 
usually exceeded before the desired directivity for 
sound of low frequencies is attained. (See Table 1.) 

The 3- and 5-ft line hydrophones are typified by 
the JP and JT hydrophones developed during World 
War II. The latter consist of nickel tubes, several 
inches in diameter and of the lengths indicated (see 
Section 12.3). The general increase in directivity 
with frequency is indicated in the table for these 


Table 1 . Estimated probable bearing error with var- 
ious hydrophones. 


Hydrophone 

Probable bearing 
error, 1 kc 
(degrees) 

Probable bearing 
error, 10 kc 
(degrees) 

3-ft line 

15.0 

1.75 

5-ft line 

9.0 

1.0 

Square piston, 1 ft 

Nondirectional 

5.25 

Rectangular piston, 3.5 ft 

13.5 

1.5 

Circular piston, 10.7 in. 

Nondirectional 

7.0 

Ring, 2 ft 

19.0 

2.0 

Ring, 8 ft 

4.5 

0.5 

Pressure gradient 

19.0 

19.0 


and the other types of hydrophones. The improved 
bearing accuracy with increasing size is also apparent. 

An exception to this rule is the pressure gradient 
hydrophone. This is a device of small dimensions, 
the directivity of which is independent of frequency. 
At low frequencies, it compares very favorably with 
much larger hydrophones of other types. 

The use of split transducer systems for listening 
was also mentioned in Chapter 14. This enables very 
good bearing accuracy to be obtained with small 
hydrophones. The binaural effect was used to obtain 
bearings during World War I. It has repeatedly been 
suggested that this might be the basis for a useful 
sonic listening system. Experimental trials have 
shown it to be capable of giving accurate bearings. It 
is doubtful whether the directivity obtained in this 
way will combat self-noise in the manner obtained 
with large hydrophones. 

i5.3 4 Ambient Noise Background 

The spectra of the various types of ambient noise 
that are encountered in listening were discussed in 
Chapter 13. Ambient noise is the limiting factor when 
the listening hydrophone is stationary, provided the 
sea state is greater than 1 or 2. For a sea state less 
than 2, the overall level of ambient noise drops below 
0 db, and thus approaches the overall level of circuit 
noise, which ranges from — 30 to 0 db; hence in this 
case the circuit noise will be limiting. Shrimp noise 
is usually negligible at lower sonic frequencies. 

15.3.5 Self-Noise Background 

The measurements of self-noise discussed in Sec- 
tion 13.3 are typical of the information available on 
this topic. The measurements have mostly been made 


274 


SONIC AND SUPERSONIC LISTENING 


for the specific purpose of evaluating a certain type 
of listening or echo-ranging system. They have 
brought to light marked differences between various 
installations of the same type of gear but have not 
resulted in a thorough understanding of the problem. 

There is great need for a thorough analysis of this 
problem. The various sources of self-noise should be 
studied in detail. In so far as the sources are electric, 
these studies should result in improved specifications 
for the ship’s wiring system, grounds for sonar gear, 
etc. The maintenance and quieting of auxiliaries is 
presumably also an important factor. It may even 
be necessary to consider the design of the ship’s hull 
and screws, and certainly the mounting and stream- 
lining of hydrophones. 

The only certain conclusion is that there is no one 
source of self-noise and that it is at present the factor 
which limits the performance of a listening system. 
Any development program must envisage an effort 
to reduce all sources of self-noise. This cannot be a 
minor part of the program, as it has in the past. Self- 
noise must be considered at all stages of the ship’s 
construction. Ideally, the ship should be built around 
the listening system ; in the past, the latter has been 
installed in the ship. The extent to which this ideal 
can be approached depends on the importance as- 
signed to listening, and this may well vary from one 
type of ship to another. 

15.3.6 Transmission Loss at 

Low Frequencies 

The experiments on the transmission of audible 
sound, described in Chapter 3, are too recent and 
incomplete to have been assimilated into a definitive 
range-prediction scheme. The data for the frequency 
range 200 to 2,000 c can be schematically summar- 
ized as in Figure 7. 

At ranges less than a few hundred yards, the trans- 
mission loss H is variable because of the interference 
between direct and surface-reflected sound. This is 
indicated by the double hatching in the figure. Be- 
yond this variable region, the transmission loss in- 
creases rapidly out to 1,000 or 2,000 yd. The fre- 
quency is a determining factor in this region, the 
higher frequencies suffering less loss than the lower 
frequencies. Downward refraction in the upper layers 
causes this loss to occur at shorter ranges, as dis- 
cussed in Chapter 3. The single hatching on Figure 7 
shows the region of rapidly increasing loss. 



Figure 7. Schematic graph of transmission loss H(r) 
for sonic sound. At ranges less than a few hundred yards, 

H is variable; this is shown by means of the double 
hatching. Beyond this variable region, the transmis- 
sion loss increases rapidly out to 1,000 or 2,000 yards; 
this region is indicated by the single hatching in the 
figure. The frequency is a determining factor in this 
region. Beyond this region, bottom-reflected sound is 
dominant, and H remains constant out to 10,000 or 
20,000 yards. (See Section 3.2.) The magnitude of H 
and the range at which it begins depend on the depth 
of the ocean. At very long ranges the transmission loss 
must again increase, but there are very few data to 
indicate the rate of increase. 

Beyond this region, bottom-reflected sound is 
dominant, and the transmission loss remains constant 
out to 10,000 or 20,000 yd. Possible reasons for this 
remarkable phenomenon have been discussed in Sec- 
tion 3.3, but there may be others as well. The mag- 
nitude of this loss and the range at which it begins 
both depend on the depth of water. A value of 80 to 
85 db appears appropriate for 1,000-fathom water. 
This value appears to be relatively independent of 
thermal conditions, but increases slightly with the 
hydrophone depth. It is also subject to irregular 
fluctuations of considerable magnitude, but they do 
not appear to bear any systematic relation to the 
range. 

At very long ranges, the transmission loss must 
again increase, but there is very little data to indicate 
the rate of increase. 

The fact that the transmission loss of bottom- 
reflected sound is nearly independent of range has 
an important bearing on the maximum ranges ob- 
tained with sonic gear. If the available signal output 
is between 60 and 80 db, the maximum range is likely 
to be less than 1,000 yd and unlikely to be greater 
than 2,000 yd. Contact will not be established until 
the target becomes audible via direct sound. But if 
the available signal output is greater than 80 db, the 
bottom-reflected sound may become useful, and the 
range may suddenly increase to 10,000 or 20,000 yd. 



SUPERSONIC LISTENING 


275 


B 



U -Q 


n 


© © -Ch 
© □ --Q-- 


u •©- -Q- ■©■ -b- ■©■ 


-B— Q- 


□ WAR PATROL REPORT, LISTENING FROM SUBMARINE 
O EXPERIMENTAL CRUISE, LISTENING FROM SUBMARINE 
-Q- WAR PATROL REPORT, L ISTENING FROM SURFACE VESSEL 
O EXPERIMENTAL CRUISE, LISTENING FROM SURFACE VESSEL 

§§ REPORTED AS AN INTERVAL 

BO DEEP WATER 
B© SHALLOW WATER 

Figure 8. Reported sonic listening ranges. (A) Unidentified targets. Listening ships; submerged submarine. (B) Target: 
destroyer, unknown speed. Listening ship: submerged submarine or stationary surface vessel. (C) Targets: freighters, 
tankers, tugs, trawlers, transports, fishing vessels. Speed not known. Listening ship: submerged submarine or sta- 
tionary surface vessel. (D) Targets: convoys, task forces. Listening ship: submerged submarine or stationary surface 
vessel. 


This critical dependence on the available signal 
output undoubtedly explains the extreme variability 
of reported sonic listening ranges. These are shown 
on Figure 8. In evaluating these data, it should be 
noted that long ranges are more likely to be reported 
than are short ranges. It thus appears that the sonic 
listening gear in present use is capable of detecting 
targets at ranges in excess of 15,000 yd under favor- 
able conditions. These are low self-noise and high 
actual output of the target. 

Transmission of the higher audible frequencies, 
above 2,000 c, presumably behaves in a manner in- 
termediate between that of frequencies below 2,000 
c, and that of the supersonic frequencies (see Section 
13.4). The effects of source directionality may in- 
crease, though this is doubtful in the case of ship 
sounds. It is therefore impossible to evaluate the 
importance of bottom reflection until further experi- 
ments have been performed. 

15.4 SUPERSONIC LISTENING 


15.4.1 Recognition 

Supersonic sound is made audible by heterodyning, 
so that the loudspeaker of the listening system emits 


audible sound. The general principles of recognition 
are thus identical with those applying to audible 
sound. However, several quantitative differences 
exist. 

In the first place, supersonic receivers usually have 
pass bands not more than 1 kc wide. The spectrum of 
the heterodyned output may thus be confined to the 
range 300 to 1,300 c, as compared to 100 to 10,000 c 
in sonic listening. 

In the second place, a 1-kc band of one supersonic 
spectrum is very similar to a 1-kc band of another. 
There are no single-frequency peaks, and while most 
spectra slope 5 to 9 db per octave the change in 
spectrum level over a 1-kc band is negligible for many 
purposes. This applies to background noise as well as 
to the sound output of ships. 

Thus, there will usually be no one frequency of the 
heterodyned sound that is more audible than another. 
There will be no tonal quality to distinguish the 
signal from the background. 

In general, the recognition differential will be zero. 
This statement requires a slight modification, since 
supersonic sound from a ship’s screw is usually rhyth- 
mically modulated in intensity. Recognition occurs 
when the maximum level of a rhythmic signal is 
equal to or possibly a few decibels less than the 
average level of nonrhythmic background. The 
maximum level of screw sounds is usually about 


276 


SONIC AND SUPERSONIC LISTENING 


3 db above the average level. Since most measure- 
ments yield average values, they must be increased 
by about 3 db in calculating the available signal. 
This increase is sometimes loosely called a recognition 
differential. 

An exception to these statements occurs when the 
target vessel is echo ranging. The pings will be heard 
as tonal pulses of sound which have a high recogni- 
tion differential (see Chapter 9), as well as a high 
source level. 

15 . 4.2 The Available Signal Level 

These considerations just presented introduce some 
simplification into the calculation of ranges. The 
spectra of the signal and the background noise need 
not be considered in detail; it is sufficient to state 
the spectrum levels at the mid-point of the listening 
band. 

With regard to background noise, the situation is 
similar to that of sonic listening. That is, if the 
listening station is quiet, the limiting factor will be 
ambient noise, whereas if listening is done from a 
noisy vessel, the noise of the listening vessel will 
predominate. In supersonic listening, however, when 
ambient noise is limiting, shrimp crackle becomes 
important. While the ordinary levels of ambient 
noise range from —78 to — 53 db depending on sea 


RANGE, YD 

100 200 500 1,000 2,000 5,000 20,000 



Figure 9. Transmission loss H(r) at 24 kc for various 
thermal conditions. The curves are based on the 
anomaly curves of Figure 14 of Chapter 3, and the 
same numbering is used. 

state, if shrimp are present the ambient noise levels 
may be —49 to —39 db. 

When used at supersonic frequencies, listening 
gear will discriminate against ambient noise. A direc- 
tivity index D of — 23 db, (equal to that of standard 
echo-ranging transducers) is common. 

i5.4 3 The Transmission Loss 

This has already been discussed in connection with 
maximum echo ranges and in Chapter 3. The graphs 


ABC 





D 



□ WAR PATROL REPORT, LISTENING FROM SUBMARINE 
O EXPERIMENTAL CRUISE, LISTENING FROM SUBMARINE 
-O WAR PATROL RE PORT, LI STENING FROM SURFACE VESSEL 
-O EXPERIMENTAL CRUISE, LI STENING FROM SURFACE VESSEL 
gg REPORTED AS AN INTERVAL 
B9 DEEP WATER 
B © SHALLOW WATER 

Figure 10. Reported supersonic listening ranges. (A) Same as Figure 8 A. (B) Same as Figure 8B. (C) Same as Figure 
8C. (D) Same as Figure 8D. 


SUPERSONIC LISTENING 


277 


of Figure 9 should be compared with Figure 7, in 
order to contrast the transmission loss of the super- 
sonic and sonic frequencies. Since there is no hori- 
zontal portion of the curve, the supersonic ranges 
should show less variation than do the sonic ranges. 
Because of this fact, also, there seems less probability 
of achieving great improvement in the performance 
of supersonic systems by a reduction in self-noise. 
However, this conclusion must be accepted with some 
caution. The source of the sound used in obtaining 
Figure 13 of Chapter 9 was an echo-ranging pro- 
jector. This discriminates strongly against transmis- 


sion via bottom reflection until relatively long ranges 
are reached. It is therefore possible that the trans- 
mission loss of supersonic ship sounds is not correctly 
given by this graph. 

The possibility of using this bottom-reflected sound 
for detection by supersonic listening has not been 
explored. It would require the use of hydrophones 
that do not discriminate against sound rays that are 
inclined at large angles to the horizontal. 

The reported ranges at which targets have been 
detected by supersonic listening gear are shown in 
Figure 10. 


























































































































































































LIST OF SYMBOLS USED 


Meanings of symbols used consistently in several different sections are listed below. Definitions 
may be found in the sections indicated. 


Section 


a Attenuation coefficient 3.2.4 

A Transmission anomaly (db) 1.3.3 

b Beam pattern function 1.2.5 

B Beam pattern function (db) 1.2.5 

c Velocity of sound in water 2.1.2 

D Directivity index (db) 7.4.3 

Z) 2 Depth at which temperature 0.3 degrees F less 

than surface temperature first occurs 2.1.5 

db Decibel, measure of sound pressure level above 

unit pressure 1.2.1 

E Sound level of echo (db) 8.1.1 

F Energy flow (watts per yd 2 ) 1.2.1 

H Transmission loss (db) 1.3.2 

I Intensity (pressure 2 ) 1.2.1 

/« Intensity on acoustic axis 1.2.5 

7i Intensity at unit range 1.2.3 

J v Volume reverberation index 5.3.4 

J R Surface reverberation index 5.3.4 

L Sound level (db) 1.2.1 

L a Source level on acoustic axis (db) 1.2.5 

L\ Source level at unit range or 1 yard (db) 1.2.3 

M Recognition differential (db) 10.3.1 


Section 

M R Recognition differential for reverberation — 


limited echoes (db) 10.3.1 

M n Recognition differential for noise-limited 

echoes (db) 10.3.1 

N Noise level (db) 9.1.3 

N(J) Noise spectrum level at/ 9.1.3 

p Pressure (dynes per sq cm) 

Q Resonance parameter 9.1.2 

r Range (yd) 

r 0 Ping length (yd) 11.3.2 

rn m Range to shadow boundary 3.2.3 

r 4 o Range at which received sound level is 40 db 

less than that received at 100 yd 3.2.3 

R (/) Response spectrum level at / 9.1.1 

RL Reverberation level (db) 5.3.4 

S Source level (db) 8.1.1 

T Target strength (db) 8.1.1 

Z Mechanical impedance 7.1.1 

X Wavelength 

n Reflection coefficient 

p Density 

r Area, cross section 


279 




BIBLIOGRAPHY 


1. 

2 . 

3. 

4. 

5. 


1 . 


2 . 


3. 


4. 


5. 


6 . 


1 . 


2 . 


Numbers such as Div. 6-540. 4-MI indicate that the document listed has been microfilmed and that 
its title appears in the microfilm index printed in a separate volume. For access to the index volume 
and to the microfilm, consult the Army or Navy agency listed on the reverse of the half-title page. 


Chapter 1 

Sonar Calibration Methods , Summary Technical Report, 
NDRC Division 6, Volume 10. 

Sonar Operator's Handbook , West Coast Sound School, 
San Diego, Calif., 1944 Edition. 

Acoustics, Alexander Wood, Interscience Publishers, 

1941. 

Acoustics , Stewart and Lindsay, D. Van Nostrand Co., 

1930. 

Theory of Propagation of Explosive Sound in Shallow 
Water, Chaim L. Pekeris, OSRD 6545, NDRC 6.1- 
srl 131-1891, CUDWR, January 1945. 

Div. 6-510. 12-M5 


Chapter 2 

The Oceans, H. U. Sverdrup, M. W. Johnson, and 
Richard H. Fleming, Prentice-Hall, 1942. 
la. Ibid., p. 790. 

Measurements of the Horizontal Thermal Structure of the 
Ocean, Norman J. Holter, Report S-17, USNRSL, 
Aug. 18, 1944. 

Div. 6-540. 4-MI 

An Acoustic Interferometer for the Measurement of Sound 
Velocity in the Ocean, Robert J. Urick, Report S-18, 
USNRSL, Sept. 18, 1944. 

Div. 6-510.22-M6 

Calculation of Sound Ray Paths in Sea Water. Theory, 
Tables and Description of a Slide Rule for Computation 
of Limiting Echo Ranges and Construction of Sound Ray 
Diagrams from Bathythermograph Observations, with 
Examples, Richard H. Fleming and Roger Revelle, 
UCDWR, Jan. 16, 1942. 

Div. 6-510. 11-M3 

The Theory of Sound, Lord Rayleigh, Macmillan Com- 
pany, 1940. 

5a. Ibid., Vol. 2, p. 131. 

The Sonic Ray Plotter, Leonard I. Schiff, NDRC 6.1- 
sr30-1741, Service Project NS-140, Report U-246, Aug. 
8, 1944. 

Div. 6-510. 11-M8 


Chapter 3 

Vibration and Sound, Philip M. Morse, McGraw-Hill 
Book Co., 1936. 

la. Ibid., p. 248. 

lb. Ibid., p. 304. 

Theory of Sound, John William Strutt and Baron Ray- 
leigh, Macmillan Company, London, 1937. 

2a. Ibid., Vol. II, pp. 215, 217. 

2b. Ibid., Vol. II, p. 319. 


3. 


4. 


5. 


6 . 

7. 


8 . 

9. 


10 . 


11 . 

12 . 


13. 


14. 


15. 


Lloyd Mirror Effect in a Variable Velocity Medium, 
Richard R. Carhart, Report M-140, UCDWR, Oct. 23, 
1943. 

Div. 6-510.111-MI 


Variation of the Sound Field Near the Surface in Deep 
Water, H. T. O’Neill and T. F. Johnston, Report U-49, 
UCDWR, Mar. 16, 1943. 

Div. 6-510. 11-M5 


Some Theoretical Studies of the Propagation of Sound in 
Shallow Water, Glen D. Camp and Carl Eckart, NDRC 
6.1-sr30-1208, Report U-102, UCDWR, Aug. 15, 1943. 

Div. 6-510. 11-M7 


Acoustics, Alexander Wood, Interscience Publishers, 
1941. 

6a. Ibid., pp. 200, 203. 


The Stability of Air Bubbles in the Sea and the Effect of 
Bubbles and Particles on the Extinction of Sound and 
Light in Sea Water, Paul S. Epstein, NDRC C4-sr30-027, 
UCDWR, Sept. 1, 1941. Div. 6 _ 540 2 1_M1 


“Absorption of Supersonic Waves in Water and Aqueous 
Suspensions,” G. K. Hartmann and Alfred B. Focke, 
The Physical Review, Vol. 57, Feb. 1, 1940, p. 221. 

Transmission of Explosive Impulses in the Sea, T. F. 
Johnston and R. W. Raitt, NDRC C4-sr30-403, Report 
U-8, UCDWR, Dec. 2, 1942. 

Div. 6-510.23-M6 


Propagation of Sound in a Medium of Variable Velocity, 
Chaim L. Pekeris, NDRC C4-sr20-001. NLL, Sept. 29, 
1941 

Div. 6-510. 11-M2 

Theory of Diffraction of Sound in the Shadow Zone, Chaim 
L. Pekeris, NDRC 6.1-sr20-846, CUDWR, May 5, 1943. 

Div. 6-510. 11-M6 


The Attenuation of Sound in the Sea, Carl F. Eckart, 
NDRC 6.1-sr30-1532, Report U-236, Service Project 
NS-140, UCDWR, July 6, 1944. 

Div. 6-510.22-M4 

Theory of Propagation of Explosive Sound in Shallow 
Water, Chaim L. Pekeris, OSRD 6545, NDRC 6.1- 
srl 131-1891, CUDWR, January 1945. 

Div. 6-510. 12-M5 

Transmission of 24-Kc Sound in Shallow Water, Report 
M-368, Service Project NObs-2074, UCDWR, Nov. 20 
1 Q4 f i 

Div. 6-510.221-M4’ • 


The Additive Effects of Wind Force, Thermal Gradient and 
Particle Size on the Transmission of 24-Kc Sound over 
Sand Bottoms in Shallow Water, Report M-375, Service 
Project NObs-2074, UCDWR, Dec. 1, 1945. 

Div. 6-510.221-M5 


281 


282 


BIBLIOGRAPHY 


16. Transmission of Sound in the Sea, E. B. Stephenson, 
S-1204, NRL, October 16, 1935. 

Div. 6-510.22-MI 

Absorption Coefficients of Sound in Sea Water, E. B. 
Stephenson, Report S-1466, NRL, Aug. 12, 1938. 

Div. 6-510.222-MI 

Absorption Coefficients of Supersonic Sound in Open Sea 
Water, E. B. Stephenson, Report S-1549, NRL, Aug. 2, 
1939. Div. 6-510.222-M2 

17. Attenuation of Underwater Sound, Frederick A. Everest 
and H. T. O’Neill, NDRC C4-sr30-494, UCDWR, 
Revised, July 30, 1942. 

Div. 6-510.2-MI 

18. Fluctuation of Transmitted Sound in the Ocean, Sonar 
Analysis Section, NDRC 6. 1-srl 131-1883, Technical 
Memorandum 6, CUDWR, Jan. 17, 1945. 

Div. 6-510.3-M4 

19. Ultrasonics and Their Scientific and Technical Applica- 
tions, Ludwig Bergmann, John Wiley and Sons, 1939. 
19a. Ibid., pp. 128-130. 

20. Transmission of 24-Kc Sound from a Deep Projector, 
Report M-408, Sonar Data Division, UCDWR, March 
1946. 

21. Attenuation and Fluctuation Studies Based on Supersonic 
Bottom Echoes, Report M-384, Service Project NObs- 
2074, UCDWR, Dec. 13, 1945. 

Div. 6-510.221-M6 

22. Acoustic Properties of Gas Bubbles in a Liquid, Part I, 
Lyman Spitzer Jr., OSRD 1705, NDRC 6. l-sr20-918, 
CUDWR, July 15, 1943. 

Div. 6-540. 22- Ml 

23. Propagation of Sound Through a Liquid Containing Bub- 
bles, Part II, Experimental Results and Theoretical Inter- 
pretation, E. L. Carstensen and Leslie L. Foldy, OSRD 
3872, NDRC 6. 1-srl 130-1629, Service Project NS-141, 
USRL, June 23, 1944. 

Div. 6-540.3-M4 


Chapter 4 

1. Military Oceanography, Summary Technical Report, 
NDRC, Division 6, Volume 6A. 

2. Long Range Sound Transmission, Maurice Ewing and 
J. Lamar Worzel, Interim Report 1, March 1, 1944, to 
January 20, 1945, WHOI, Aug. 25, 1945. 

Div. 6-510.1-M4 

3. Oceanography for Meterologists, H. U. Sverdrup, Prentice- 
Hall, 1942. 

3a. Ibid., Chapter 4. 

3b. Ibid., Chapter 6, pp. 123, etc. 

4. The Oceans, H. U. Sverdrup, M. W. Johnson, and 
Richard H. Fleming, Prentice-Hall, 1942. 

4a. Ibid., Figures 210 and 212, pp. 748 and 753. 


Chapter 5 

1. Theory of Sound, John William Strutt and Baron Ray- 
leigh, Macmillan Company, 1937, Vol. II, p. 283. 

la. Ibid., Vol. I, p. 41. 

2. “On the Absorption of Sound Waves in Suspensions and 
Emulsions,” Paul S. Epstein, Theodore von Karman 
Anniversary Volume, CIT, May 11, 1941, pp. 162-168. 

3. The Stability of Air Bubbles in the Sea and the Effect 
of Bubbles and Particles on the Extinction of Sound and 
Light in Sea Water, Paul S. Epstein, OSRD C4-sr30-027, 
UCDWR, Sept. 1, 1941. 

Div. 6-540.21-MI 

4. Dissipation of Energy due to the Presence of Air Bubbles 
in the Sea, F. H. Willis, OSRD C4 — British — 503. 
Comment, Conyers Herring, CUDWR — Special Studies. 

Div. 6-540.2-M3 

5. Acoustic Properties of Gas Bubbles in a Liquid, Lyman 
Spitzer, Jr., OSRD 1705, NDRC 6.1-sr20-918, CUDWR, 
July 15, 1943. 

Div. 6-540. 22-MI 

6. Propagation of Sound Through a Liquid Containing 
Bubbles, Part I, General Theory, Leslie L. Foldy and 
E. L. Carstensen, OSRD 3601, NDRC 6. 1-srl 130-1378, 
Service Project NS-141, USRL, Apr. 25, 1944. 

Div. 6-540. 22-M 2 

7. Reflection and Scattering of Sound, F. H. Willis, OSRD 
WA-92-10f, NDRC C4-brTS-501, British Internal Re- 
port 50, HM A/SEE, Fairlie Laboratory, Great Britain, 
Dec. 20, 1941. 

Div. 6-530. 1-MI 

8. The Discrimination of Transducers Against Reverbera- 
tion, OSRD 1761, NDRC 6.1-sr30-968, Report U-75, 
UCDWR, May 31, 1943. 

Div. 6-520. 1-M8 

9. The Detection of an Echo in the Presence of Reverberation , 
Carl F. Eckart, OSRD 173, NDRC C4-sr30-175, 
UCDWR, May 12, 1942. 

Div. 6-560. 32-MI 

10. Reverberation Studies at 24 Kc, OSRD 1098, NDRC 
C4-sr30-401, Report U-7, UCDWR, Nov. 23, 1942. 

Div. 6-520-M2 

11. Frequency Characteristics of Echoes and Reverberation, 
W. M. Rayton and Raymond C. Fisher, OSRD 4159, 
NDRC 6.1-sr30-1740, Service Project NS-140, Report 
U-244, UCDWR, Aug. 9, 1944. 

Div. 6-520.3-M2 

12. The Attenuation of Sound in the Sea, Carl F. Eckart, 
NDRC 6.1-sr30-1532, Service Project NS-140, Report 
U-236, UCDWR, July 6, 1944. 

Div. 6-510.22-M4 

13. Stratification of Sound Scatterers in the Ocean, George E. 
Duvall, Service Project NObs-2074, Report M-397, 
UCDWR, Feb. 16, 1946. 


Div. 6-520. 22-M3 


BIBLIOGRAPHY 


283 


14. Forward Scattering from the Deep Scattering Layer , 
Richard R. Carhart, Service Project NObs-2074, Report 
M-398, UCDWR, Mar. 19, 1946. 

Div. 6-520. 22- M4 

Chapter 6 

1. Laboratory Studies of the Acoustic Properties of Wakest 
Parts I and II, Jeffries Wyman, Wendel Lehmann, and 
David Barnes, NDRC 6.1-sr31-1069, Service Project 
NS-141, Apr. 3, 1944. 

Div. 6-540.3-M3 

2. “On the Destructive Action of Cavitation,” Kornfeld and 
Suvorav, Journal of Physics of USSR, Vol. 7, No. 3, 1944, 
pp. 171-181. 

3. Propagation of Sound Through a Liquid Containing 
Bubbles, Part I, General Theory, Leslie L. Foldy, OSRD 
3601, NDRC 6. 1-sr 1130-1378, Service Project NS-141, 
USRL, Apr. 25, 1944. 

Div. 6-540.22-M2 

Part II, Experimental Results and Theoretical Interpreta- 
tion, E. L. Carstensen and Leslie L. Foldy, OSRD 3872, 
NDRC 6. 1-sr 1130-1629, Service Project NS-141, USRL, 
June 23, 1944. 

Div. 6-540.3-M4 

4. Sound Transmission Through Destroyer Wakes, OEMsr- 
30, Service Project NS-141, Report M-189, UCDWR, 
Mar. 8, 1944. 

Div. 6-540. 32-M3 

5. Echoes from Wakes, Carl F. Eckart, NDRC C4-sr30-498, 
UCDWR, Aug. 29, 1942. 

Div. 6-540.31-MI 

6. Acoustic Measurements of Surface Wakes in San Diego 
Harbor, Richard R. Carhart and George E. Duvall, 
OSRD 1628, NDRC 6.1-sr30-961, Report U-62, 
UCDWR, May 8, 1943. 

Div. 6-540. 32-MI 

Chapter 7 

1. “On the Effects of Magnetism upon the Dimensions of 

Iron and Steel,” J. P. Joule, The London , Edinburgh and 
Dublin Philosophical Magazine and Journal of Science, 
Vol. 30, 1847, p. 76. 

2. Magnetostrictive Transducers, Malcolm H. Hebb and 
Harvey Brooks, NDRC 6. l-sr287-898, HUSL, June 22, 
1943. 

Div. 6-612. 1-M2 

3. Design and Construction of Magnetostriction Transducers , 
Summary Technical Report, NDRC, Division 6, Volume 
13. 

4. Sonar Operator's Handbook, West Coast Sound School, 
San Diego, Calif., 1944 Edition 

5. J. and P. Curie, Comptes Rendus Acadamie Sci., Paris, 
Vol. 91, 1880, p. 294 and Vol. 93, 1881, p. 1137. 

6. “Uses and Possibilities of Piezoelectric Oscillators,” A. 
Hund, Proceedings of the Institute of Radio Engineers, 
Vol. 14, 1926, p. 447. 


7. Design and Construction of Crystal Transducers, Summary 
Technical Report, NDRC Division 6, Volume 12. 

8. A Practical Dictionary of Underwater Acoustical Devices 
(Volume 1 and Supplementary Loose Leaf Sheets), 
OSRD 772, NDRC 6.1-sr20-889, CUDWR-USRL, July 
27, 1943. 

Div. 6-554-M28 

9. Vibration and Sound, Philip M. Morse, McGraw-Hill 
Book Co., New York, 1936. 

10. Loudspeakers, Norman W. McLachlan, Oxford, Claren- 
den Press, 1934. 

Chapter 8 

1. Reflections from Submarines at Close Ranges, Model Ex- 
periments Using Optical Method, Service Project NS-222 
and MIT Research Project DIC-6187, MIT, Apr. 8, 
1944. 

Div. 6-530. 23-M2 

2. Studies of Optical Reflections from Submarine Models 
(Part I), OSRD 3706, NDRC 6.1-srl046-1053, Service 
Project NS-222, Research Project DIC-6187, MIT, 
Apr. 12, 1944. 

Div. 6-530. 23-M3 

3. Studies of Optical Reflections from Submarine Models 
(Part II), OSRD 3706, NDRC 6. 1-sr 1046- 1668, Service 
Project NS-222, Research Project DIC-6187, MIT, 
Aug. 15, 1944. 

Div. 6-530. 23-M4 

4. Some Measurements of the Directivity Patterns, Target 
Strengths, and Directivity Factors of Spheres, Discs, Tri- 
planes, and Polyplanes, C. J. Burbank and Raymond 
C. Fisher, File 02.133, UCDWR Report C-81, Calibra- 
tion Group, UCDWR at the USNRSL, San Diego, 
California, Aug. 2, 1945. 

Div. 6-633.2-M6 

5. Reflection of Light from a Submarine Model, R. B. Tib- 
bey, Report M-61, UCDWR, May 12, 1943. 

Div. 6-530. 23-MI 

6. Measurement of Reflections from Submarines Using 
Models and High Frequency Sound, Joseph B. Keller, 
OSRD 4439, NDRC 6. 1-srl 130-1834, Service Project 
NS- 140, USRL, Sept. 27, 1944. 

Div. 6-530. 23-M5 

7. Physics of Sound in the Sea, Summary Technical Report, 
NDRC Division 6, Volume 8. 

Chapter 9 

1. Computed Maximum Echo and Detection Ranges for Sub- 
marine Echo-Ranging Gear, NDRC 6. 1-srl 128, 1131- 
1688, CUDWR, July 1944. 

Div. 6-570-M2 

2. Self-Noise of Sonar Gear, OEMsr-1131, OEMsr-1483, and 
NObs-2083, Report C-2(0. 1.332), SAG-WHOI, August 
1, 1946. 


Div. 6-580. 32-MI 


284 


BIBLIOGRAPHY 


3. Status Report on Task No. 5, Effect of Short Pulse Length 
and Receiver Bandwidth on Echo Ranging , Robert W. 
Kirkland, Report 3510-RWK-HP, BTL, July 15, 1944. 

Div. 6-632. 03-M5 

4. Interim Report on Electronic Own Doppler Nullifier, 
A. Wilson Nolle and W. A. Felsing, NDRC 6.1-sr287-719, 
HUSL, Mar. 24, 1943. 

Div. 6-631. 31-M5 

5. Dependence of Operational Efficacy of Echo-Ranging Gear 
on its Physical Characteristics , Henry Primakoff and 
Martin J. Klein, Service Project NS-182, NDRC 

6. 1- srl 130-2141, CUDWR, USRL, Mar. 15, 1945. 

Div. 6-551-M14 

6. A Survey of the Problem of Maximum Echo Ranges (Pre- 
liminary Draft), Carl Eckart, NDRC 6.1-sr30-1315, 
Report U-130, UCDWR, Nov. 20, 1943. 

Chapter 11 

1. Bearing Deviation Indicator , OSRD 6425, NDRC 

6.1- sr287-2075, HUSL, Nov. 1, 1945. 

Div. 6-631.4-MI 

2. “FM Sonar Joins the Fleet,” Lt. J. J. Crowley, USNR, 
BuShips Electron , NavShips 900,100, September 1945. 

3 Frequency Modulation Sonar, Malcolm C. Henderson and 
Charles A. Hisserich, OEMsr-30, Report U-95, UC- 
DWR, Sept. 4, 1943. 

Div. 6-635.241-M3 

4. Frequency Modulation Echo-Ranging Systems, Cobar, 
Pribar, and Subsight, Malcolm C. Henderson, NDRC 

6. 1- sr30-408, Report U-12, UCDWR, Dec. 30, 1942. 

Div. 6-635.2-MI 

5. Underwater Sound Equipment IV — Frequency Modulated 
Sonar Systems, Summary Technical Report, NDRC 
Division 6, Volume 17. 

6. Instruction Book for QLA and QLA-1 Sonar Equipment, 
Service Project NObs-2074, Report NavShips 900,790, 
UCDWR, Feb. 27, 1946. 

Div. 6-635.3-MI 

7. Doppler Effect in FM Sonar, Malcolm C. Henderson, 
OSRD 1955, NDRC 6.1-sr30-1115, Report U-107, 
UCDWR, Sept. 20, 1943. 

Div. 6-635. 12-M4 

Doppler Effect in Frequency Modulation Sonar, Mathe- 
matical Appendix, Malcolm C. Henderson, OEMsr-30, 
Service Project NS-142, Report M-184, UCDWR, 
Feb. 8, 1944. 

Div. 6-635. 12-M5 

8. A Practical Dictionary of Underwater Acoustical Devices, 
Cards 120 and 121, OSRD 772, USRL, July 27, 1943. 

Div. 6-554-M28 


9. Status Report on Echoes from Small Objects, Report 
M-388, Sonar Data Division, UCDWR, Feb. 14, 1946. 

10. T ime V ariation of Gain for QC Receivers ( Memorandum) , 
J. Lewis Hathaway, HUSL, Dec. 8, 1942. 

11. Automatic Gain Control in Echo-Ranging Systems, Fred- 
erick V. Hunt, NDRC 6.1-sr287-764, HUSL, Apr. 13, 
1943. 

Div. 6-631. 13-MI 

12. Automatic Frequency Response Recorder, Alfred K. 
Tatum, Report P35/671, NLL, Dec. 22, 1943. 

Div. 6-553.5-MI 

Chapter 12 

1. Installation, Operation and Maintenance Instructions for 
Model JP-1 Sound Receiving Equipment, Topside Sonic 
Listening Equipment, Service Project NS-113, Report 
D24/417, CUDWR-NLL, Sept. 1, 1943. 

Div. 6-623. 1-MI 

2. Noise Level Monitor and Cavitation Indicator, William B. 
Snow, OSRD 4685 NDRC 6. 1-srl 128-1930, Service 
Project NS-113, Report P55/1281, NLL, Jan. 31, 1945. 

Div. 6-642. 1-M3 

3. How to Operate the Noise Level Monitor and the Cavitation 
Indicator, OEMsr-1128, Report P55/1191, CUDWR- 
NLL, Feb. 1, 1945. 

4. Underwater Sound Output of USS Tinosa (SS 283). 
Report M-303, UCDWR, Mar. 5, 1945. 

Div. 6-580. 1-M11 

5. Survey of Underwater Sound. Sounds from Submarines, 
Vern O. Knudsen, R. S. Alford, and J. W. Emling, 

6.1-NDRC-1306, Report 2, Dec. 31, 1943. 

Div. 6-580. 1-M2 

6. The Acoustic Fields of Ships of Various Kinds as De- 
termined on the Mark 2 Acoustic Range at Wolf Trap, 
Report 700, NOL, Mar. 25, 1943. 

Div. 6-580.2-MI 

7. Survey of Underwater Sounds. Sounds from Surface 
Ships, M. T. Dow, J. W. Emling, and Vern O. Knudsen, 
OSRD 5424, NDRC 6.1-2124, Report 4, June 15, 1945. 

Div. 6-580. 2-M7 

8. Acoustic Measurements ( 75-150 cps ) on Escort Vessels at 
Treasure Island, California, Joseph Ashbrook, Report 
AAR-35, U. S. Navy Department, Bureau of Ordnance, 
Dec. 1, 1944. 

Div. 6-580.2-M5 

9. The Sound Spectrograph, A Time-Frequency-Intensity 
Analyzer, OEMsr-435, BTL, Oct. 1, 1943. 

Div. 13-302. 1-M2 

10. A Practical Dictionary of Underwater Acoustical De- 
vices (Volume 1 and Supplementary Loose Leaf Sheets), 
OSRD 772, NDRC 6.1-sr20-889, CUDWR— USRL, 
July 27, 1943. 


Div. 6-554-M28 


BIBLIOGRAPHY 


285 


Chapter 13 

1. Sound Survey, San Francisco Harbor during November, 
1942, Report U-27, UCDWR, Feb. 3, 1943. 

Div. 6-580. 33-MI 

2. Radio Engineers’ Handbook, F. E. Terman, McGraw- 
Hill Book Co., 1943. 

2a. Ibid., p. 476. 

3. JJSS Shark — Noise vs Speed Tests, William B. Snow and 
Henry B. Hoff, Report P32/P33/R812, NLL, Apr. 12, 
1944. 

Div. 6-580. 1-M5 

4. Sound Cavitation Tests on USS Springer ( SS 414), Lab- 
oratory Report M-283, UCDWR, Dec. 20, 1944. 

Div. 6-580. 1-M9 

5. Survey of Underwater Sound, Ambient Noise, Vern O. 
Ivnudsen, R. S. Alford, and J. W. Ending, 6.1-NDRC- 
1848, Report 3, Sept. 26, 1944. 

Div. 6-580. 33-M2 

6. Self-Noise in Sonar Gear, OEMsr-1131, OEMsr-1483, 
and NObs-2083, Report C-2 (01.332), WHOI, Aug. 1, 
1946. 

Div. 6-580. 32- Ml 

Chapter 14 

1. “Auditory Patterns,” Harvey Fletcher, Reviews of 
Modern Physics, Vol. 12, January 1940, p. 47. 

2. “Differential Pitch Sensitivity of the Ear,” E. G. Shower 
and R. Biddulph, The Journal of the Acoustical Society 
of America, Vol. Ill, 1931, pp. 275-287. 

3. Tone Duration as a Factor in Pitch Discrimination, 
E. G. Wever, Report M-179, UCDWR, Feb. 16, 1944. 

Div. 6-560. 1-M4 

4. “Differential Intensity Sensitivity for Pure Tones,” 
R. R. Riesz, The Physical Review, Ser. II, Vol. 31, 1928. 

5. “Theory of Hearing: Vibration of Basilar Membrane; 
Fatigue Effect,” G. V. Bekesy, Physikalische Zeitschrift, 
March 1929, p. 118. 

6. Hearing, Its Psychology and Physiology, S. Smith Stevens 
and Hallowell Davis, John Wiley and Sons, 1938, p. 223. 

7. Speech and Hearing, Harvey Fletcher, D. Van Nostrand 
Co., 1929. 

8. “Loudness, Masking, and their Relation to the Hearing 
Process and the Problems of Noise Measurements,” 
Harvey Fletcher, The Journal of the Acoustical Society 
of America, Vol. 9, 1938, p. 282. 


9. Masking Experiments, Part I, NDRC 6.1-sr30-1751, 
Report U-229, Service Projects NO-163 and NS-164, 
UCDWR, June 28, 1944. 

Div. 6-560. 2 1-M4 

10. Masking Experiments, Part II, NDRC 6.1-sr30-1757, 
Report U-258, Service Projects NO-163 and NS-164, 
UCDWR, Sept. 15, 1944. 

Div. 6-560.21-M6 

Chapter 15 

1. Sonic Listening Aboard Submarines, OSRD 5311, NDRC 
6. 1-srl 131-1885, Service Project NS-140, Sonar Analysis 

. Section, CUDWR, February 1945. 

Div. 6-623. 1-M8 

2. Basic Factors Affecting the Performance of Sonic Listen- 
ing Gear on Submarines, OSRD 5031, NDRC 6. 1-srl 131“ 
1888, Service Project NS-140, CUDWR, February, 1945. 

Div. 6-623. 1-M9 

3. Comparative Tests on Submarine and Surface Craft Lis- 
tening Equipments, Donald P. Loye and Ralph C. 
Maninger, NDRC 6.1-sr20-1020, Service Project NS-113, 
Report D24/D38/391, NLL, Sept. 10, 1943. 

Div. 6-623-M4 

4. Maximum Listening Ranges of Underwater Sound Equip- 
ment, Ralph C. Maninger, Report P33/R794, NLL, 
Mar. 13, 1944. 

Div. 6-570. 22-MI 

5. Addendum I to Maximum Listening Ranges of Under- 
water Sound Equipment (Report P33/R794), LeRoy A. 
Woodward, Report P33/R1008, NLL, July 1, 1944. 

Div. 6-570. 22-M2 

6. A Study of Binaural Perception of the Direction of a 
Sound Source, Irving Langmuir, Vincent J. Schaefer, 
and others, OSRD 4079, NDRC 6.1-sr323-1840, General 
Electric Company, June 30, 1944. 

Div. 6-560. 1-M5 

7. Experimental Investigation of Factors Involved in Sonic 
Listening, Ralph C. Maninger, NDRC 6. 1-srl 128-1932, 
Report P33/1319, NLL, Feb. 28, 1945. 

Div. 6-62 1-M7 

8. Prediction of Sonic and Supersonic Listening Ranges, 
NDRC 6. 1-srl 131-1884, Service Project NS-140, 
CUDWR, December 1944. 


Div. 6-570. 1-M6 


CONTRACT NUMBERS, CONTRACTORS, AND SUBJECT OF CONTRACTS 


Contract 

Number 

Name and Address 
of Contractor 

Subject 

OEMsr-20 

The Trustees of Columbia University in the 
City of New York 

New York, New York 

Studies and experimental investigations in connection with 
and for the development of equipment and methods 
pertaining to submarine warfare. 

OEMsr-1131 

The Trustees of Columbia University in the 
City of New York 

New York, New York 

Conduct studies and investigations in connection with the 
evaluation of the applicability of data, methods, devices, 
and systems pertaining to submarine and subsurface 
warfare. 

OEMsr-30 

The Regents of the University of California 
Berkeley, California 

Maintain and operate certain laboratories and conduct 
studies and experimental investigations in connection with 
submarine and subsurface warfare. 

OEMsr-31 

Woods Hole Oceanographic Institution 
Woods Hole, Massachusetts 

Studies and experimental investigations in connection with 
the structure of the superficial layer of the ocean and its 
effects on the transmission of sonic and supersonic 
vibrations. 

OEMsr-287 

President and Fellows of Harvard College 
Cambiidge, Massachusetts 

Studies and experimental investigations in connection with 
(i) the development of equipment and devices relating 
to subsurface warfare. 


286 


SERVICE PROJECT NUMBERS 


The projects listed below were transmitted to the Executive Secretary, 
NDRC, from the War or Navy Department through either the War 
Department Liaison Officer for NDRC or the Office of Research and 
Inventions (formerly the Coordinator of Research and Development), 
Navy Department. 


Service 

Project 

Number 

Subject 

NO-222 

Acoustic reflection fields of submarines 

NS-140 

Acoustic properties of the sea bottom 

Ext. 


NS-140 

Range as function of oceanographic factors 

NS-141 

Acoustic properties of wakes 


S' 





287 




















































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' 




































' 































INDEX 


The subject indexes of all STR volumes are combined in a master index printed in a separate volume. For 
access to the index volume consult the Army or Navy Agency listed on the reverse of the half-title page. 


Absorption of sound 
air bubbles, 55 
causes, 55-57 
definition, 9, 55 

ship wakes, 123-124, 125, 127-128 
Acoustic projectors 
see Projectors, sonar 
Acoustic shadow in ocean 
diffraction, 33 
ECR layer, 112-113 
formation, 83 
limiting range, 32 
scattering of sound, 33 
sound intensity, 26-27 
theory, 16-17 

ADP projectors (ammonium dihydro- 
gen phosphate), 140-141, 148 
Air bubbles in ocean 
as deceptive target, 174 
attenuation of sound, 57 
sound absorption, 57 
target area, 85-86 
wakes from ships, 122, 126-127 
Airborne noise, 243 
Ambient noise, 248-254 
biological noise, 250-254 
from harbors, 253 
general character, 249 
in echo ranging, 182-184 
sea noise, 249-250 
sonic listening, 273 
sources, 248 

Ammonium dihydrogen phosphate pro- 
jectors, 140-141, 148 
Amplification ratio, 177 
Amplifiers, response curves, 177 
ARSB (anchored radio sono buoy), 223 
Asdic projector, 139-141, 147 
Attenuation of sound, 34-36, 55-60 
air bubbles, 57 
causes, 55-58 
coefficient, 9, 34-36, 57 
definition, 7 

depth of hydrophone, 34 
fresh water, 57 
minimal coefficient, 58-60 
recommendations, 57 
reverberation, 108 
scattering, 103 
thermal gradients, 58 
thermocline layer, 34 
transmission, 7, 9 
vertical pulsing, 59-60 
viscosity, 57-58 
Auditory masking 
see Masking, auditory 


Autocorrelation coefficient of signals, 
63-64 

A VC (automatic volume control) in 
sonar receivers, 220 

Bathythermograph measurements 
description of instrument, 11-12 
isothermal layer, 13 
isotherms, 74 

positive and negative temperature 
gradients, 12 

temperature-depth graphs, 12-13 
thermocline layer, 13 
BDI (bearing deviation indicator), 209- 
210 

TVG control, 210 
Beam patterns of transducers 
see Directivity in sonic listening 
Bearing deviation indication, 207-210 
definition of bearing deviation, 205 
devices, 207 
split transducer, 207 
standard BDI, 209-210 
Bearing of target 
see Target bearing 
Bell Telephone Laboratories, 239 
Biological noise, 250-254 
fish choruses, 252-253 
shrimps, 251-252 
sources, 250 

Bottom reverberation, ocean, 88-90, 
109-112 

effects of refraction, 110-111 
reverberation levels, 111-112 
scattering coefficients, 90, 112 
transmission loss, 109-110 
types of sea bottom, 109 
British Asdic projector, 139-140, 147 
Bubbles in ocean 

as deceptive target, 174 
attenuation of sound, 57 
sound absorption, 57 
target area, 85-86 
wakes from ships, 122, 126-127 
Buoy, anchored radio sono, 223 

Capacitive rotation sonar, 212-213 
comparison with FM sonar, 218-219 
Cavitation 

effect on projector power output, 148 
effect on wake echoes, 120-122 
from submarines, 231, 232 
from surface ships, 237 
Circuit noise, 245-246 
hum, 246 
microphonics, 246 


sources, 245 
spectrum, 245 
thermal, 245 
tubes, 246 
Circuits, electronic 

AVC sonar receivers, 220 
reverberation-controlled gain, 220 
time varied gain, 220 
Cochlea of ear, 256 

Compression wave, underwater explo- 
sions, 23 

Convective overturn of ocean layers, 71 
Cooling of ocean, 71, 76-77 
effective back radiation, 76 
evaporation, 77 
incoming radiation, 76 
CR sonar (capacitive rotation) , 212-213 
comparison with FM sonar, 218-219 
Crystals, piezoelectric in projectors, 
138-141 

quartz projectors, 139-140 
Rochelle salt and ADP projectors, 
140-141 
theory, 138 
tjrpes, 138 

Currents, effect on ocean temperature, 
72, 78-79 

divergence and convergence of sur- 
face currents, 79 
drift currents, 78 
internal waves, 79 
permanent currents, 78-79 
tidal currents, 79 

Density of sea water, 69 
Depth determination of targets, 221 
Diffraction of underwater sound, 33 
Dipole effect in sound transmission, 24- 
25, 44-48 

refraction, 25, 46-48 
sonic frequencies, 45 
sound transmission, 45-46 
Directivity in sonic listening, 141-146, 
272-273 

beam pattern correction, 90 
directivity index, 146-147, 180, 229 
directivity patterns of transducers, 
5-6, 143-146, 228-229 
probable bearing error, 273 
submarine sounds, 234-235 
Distortion in signals, 60-62, 226 
Domes, acoustic effect on projector, 
150-152 

Doppler effect, 193-195 
echo ranging, 194 
FM scanning sonar, 217-218 


289 


290 


INDEX 


formula for doppler shift, 193 
hydrophones, 179-180 
own-doppler nullifier, 180 
reverberation, 179 
target doppler, 194 
theory, 193-194 
up-and down-doppler, 194 
Double-source effect in sound trans- 
mission, 24-25, 44-48 
refraction, 46-48 
sonic frequencies, 45 
sound transmission, 45-46 
Drift currents, ocean, 78 

Ear, human, 255-260 
anatomy, 255-256 
binaural effect, 259-260 
masking, 258 

psychological characteristics of 
sound, 258-260 
sensitivity, 257 
threshold of hearing, 258 
Echo, 83-85, 165-174 
see also Reverberation 
energy flow, 83 
envelopes of echoes, 165-167 
formula for echo level, 84 
from artificial targets, 170-174 
from ocean bottom and surface, 24, 
36 

from small particles, 84-85 
from wakes, 120-122, 130, 170 
intensity, 83-84, 154, 158, 167-169 
ping length, 165-169, 187-188, 197- 
198, 219-220 

reverberation ratio, 219-220 
scattering of sound, 83-84 
target area and strength, 83, 84 
theory, 59-60, 83-84 
travel time, 87 
Echo ranging 

see also Hydrophones; Projectors, 
sonar 

comparison with listening, 223 
doppler effect, 194 
general discussion, 133 
noise background, 182-184, 189-191 
range calculation, 189-191, 196-199, 
267-268 

reverberation, 192-193, 195-199, 219- 
220 

target strength, 153-174 
Echo ranging applications, 200-221 
scanning sonar, 210-219 
search operations, 200-204 
small object detection, 219-220 
target bearing, 204-210 
target depth determination, 221 
target detection, 201-203 
Echo ranging signal, 148-150 
frequency, 148-150 


keying length and interval, 150 
Echo recognition, 184-189 
aural recognition, 195-196 
definition of recognition, 184 
effect of ping length, 187-188 
effect of reverberation, 195-196 
multiple pulses, 188 
range recorder, 185 
recognition differential, 184-185, 188- 
189, 195 

recognition level, 186 
recognition probability, 188-189 
Echo repeater, 153 
ECR ocean layer 
acoustic shadow, 112-113 
diurnal cycle, 101 
reverberation, 108, 112-113 
Electronic rotation sonar, 212-213 
Energy of sound field, 1-2, 83 
ER sonar (electronic rotation), 212-213 
ERSB (expendable radio sono buoy), 
223 

Evaporation in ocean, 77 
Explosions underwater 
see Underwater explosions 

FM scanning sonar, 214-219 
application to fire control problems, 
218 

comparison with CR sonar, 218-219 
doppler range error, 217-218 
echo duration, 216 
effective ping length, 216 
principles of operation, 214-215 
range and bearing indication, 216 
target range and echo frequency, 
215-220 
Formulas 

attenuation coefficient, 57 
beam pattern of sound source, 6 
directivity index of a projector, 146 
doppler shift, 193 
echo level, 84 

echo ranging target strength, 153 
echo recognition differential. 184 
efficiency of a projector, 147 
energy flow of echoes, 83 
energy of sound field, 1-2, 4 
inherent threshold of hydrophone, 
181 

intensity of bottom reflected sound, 
49 

intensity of volume reverberation, 
87-88 

mechanical impedance of projectors, 
135 

pressure in reflected sound wave, 45 
radiation impedance of projectors, 
135 

Rayleigh formula, reverberation, 92 


recognition differential for reverber- 
ation, 195 

recognition level for noise and rever- 
beration, 197 

reverberation level, 90, 111 

sound intensity, 2 

sound level, 2 

strength of wake, 125 

target strength of sound scatterer, 84 

Harvard Underwater Sound Labora- 
tory, 209 

Hearing process, 255-265 
auditory masking, 260-265 
binaural effects, 259-260 
human ear, 255-260 
psychological characteristics, 258-260 
theory, 256-257 
threshold of hearing, 258 
Heating of ocean, 71, 76-77 
effective back radiation, 76 
incoming radiation, 76 
negative gradients, 71 
Helmholtz theory of hearing, 256 
Hydrophones, 175-182 

automatic volume control, 220 
characteristics, 227 
dependence of attenuation on depth, 
34-36 

dependence of transmission on depth, 
31-32, 43, 51-52 
directivity, 228-229 
directivity index, 146, 180, 229 
discrimination against noise, 180 
doppler effect, 179-180 
inherent threshold, 181 
JK hydrophone, 230 
JP hydrophone, 229 
magnetostriction, 229, 232 
multiple hydrophones, 205-207 
noise from, 247 
operation, 175-176 
own-doppler nullifier, 180 
response, 176-179, 227 
reverberation, 179-180 
self-noise, 246 

specifications, 181-182, 266-267 

spectrum level, 177-178 

time varied gain, 220 

tuning, 175, 179-180 

use of multiple hydrophones, 203-207 

Image effect in sound transmission, 24- 
25, 44-48 

refraction, 25, 46-48 
sonic fequencies, 44 
Impedance of projectors, 135-136 
mechanical impedance, 135 
radiation impedance, 135-136 
Intensity of sound 
see Sound level 


INDEX 


29 L 


Invar for magnetostriction projectors, 
137 

Isothermal layer in the ocean, 16-17 
definition, 13 

effect on supersonic frequencies, 31 
formation, 80 

Isotherms (temperature curves), 74 

Japanese listening gear, 230 

JP hydrophone, 229-230 
amplifier, 229 
directivity pattern, 229 

Listening, 223-224, 227-230, 266-277 
see also Hearing process; Hydro- 
phones 

applications, 223-224 
background noise, 243-254, 272-275 
basic factors, 224 

comparison with echo ranging, 223 
enemy listening gear, 230 
frequency range, 266 
maximum range, 266-272 
objectives of sound operator, 223 
sonic frequencies, 272-275 
supersonic frequencies, 275-277 

Listening range equations, applica- 
tions, 269-272 

choice of listening band, 270-271 
range prediction problem, 271-272 
reduction of noise background, 269- 
270 

reduction of sound output for de- 
fense, 269 

Lloyd mirror effect in sound transmis- 
sion, 24-25, 44-48 
refraction, 25, 46-48 
sonic frequencies, 44 
sound transmission, 45-46 

Lobe suppression, directivity patterns, 
143 

Magnetostriction hydrophones, 229, 
232 

Magnetostriction projectors, 137-138 
maximum voltage, 148 
oscillator, 137 
polarizing current, 137-138 
production of sound waves, 138 
theory, 137-138 
use of nickel, 137 

Masking, auditory, 260-261 
adjacent masking, 263-265 
by complex sound, 262-263 
by pure tone, 261-262 
definition, 258 
effect of receiver, 265 
probability of signal recognition, 260 
theory, 261 

threshold of masking, 260-261 
variable levels, 265 


Massachusetts Institute of Technology, 
159 

Microphonics in circuits, 246 
Monel for magnetostriction projectors, 
137 

Naval Research Laboratory, 148 
Navy Radio and Sound Laboratory, 44 
Negative gradients in the ocean 
cause, 71, 81 
definition, 13 
depth, 72 

effect on supersonic frequencies, 31 
geographical location, 78 
intensity of sound, 26 
limiting range, 32 

Nickel for magnetostriction projectors, 
137 

NLM (noise level monitor), 232 
Noise background, echo ranging, 182- 
184, 189-191 
ambient noise, 182-184 
effect on range calculation, 189-191 
equipment noise, 183-184 
general classification, 182-183 
Noise background, listening, 243-254 
airborne, 242 
ambient noise, 248-249 
circuit noise, 245-246 
classification of noise, 243-245 
equipment noise, 246-248 
overall levels of background noise, 
244-245 

reduction, 269-270 
sonic frequencies, 269-270, 272-275 
Noise level monitor, 232 

Ocean bottom 
echoes, 36 

effect on transmission, 40-41 
reflected sound, 36-37, 44, 48-50, 59 
reverberation, 109 
Ocean depth 

effect on reverberation, 99-109 
effect on sound attenuation, 34 
effect on transmission, 30-32, 39-44 
Ocean temperature 

convective overturn, 71 
isothermal layer, 13, 16-17, 31, 74, 80 
mixed layer, 34 

negative gradients, 71-72, 78, 81 
positive gradients, 71, 81 
stability, 69-71 
theory, 17, 21 

thermocline, 13, 16-17, 31, 34 
Oceanography, 68-81 
acoustic properties, 6-7 
acoustic shadow, 16-17, 26-27, 32-33, 
83, 112-113 
air bubbles, 57, 86 
currents, 72, 78-79 


density of sea water, 69 
geographical variations, 79-81 
recommendations for future research, 
33-34 

salinity of sea water, 69 
temperature factors, 68-79 
ODN (own-doppler nullifier), 180 
Oscillograms 

reverberation, 91, 94, 98 
sound transmission underwater, 60, 
226 

Ossicles of ear, 256 
Own-doppler nullifier, 180 

PAL (phase-actuated locator), 207 
Periodmeter, measurement of rever- 
beration distortion, 95-97 
Permendur for magnetostriction pro- 
jectors, 137 

Phase-actuated locators, 207 
Piezoelectric projectors, 138-141, 147- 
148 

materials used, 138 
quartz projectors, 139-140 
Rochelle salt and ADP projectors, 
140-141 

theory, 138-139 
Ping length 
definition, 87-88 

effect on echoes, 165-169, 187-188, 
197-198, 219-220 

effect on reverberation, 87-88, 92, 
95, 219-220 

effect on wake echoes, 130 
FM scanning sonar, 216 
small object detection, 219-220 
Pinna of ear, 255 
Plan position indicator, 212-213 
“Pokes” of sound, 23 
Positive gradients in the ocean, 71, 81 
PPI (plan position indicator), 212-213 
Pressure level of sound, 1-2 
Projectors, sonar, 135-152 
acoustic axis, 146 
basic principles, 135 
characteristics of standard projec- 
tors, 147 

directivity, 90, 141-146 
effect of cavitation, 148 
effect of domes, 150-152 
impedance, 135-136 
limitation of power output, 148 
magnetostriction projectors, 137- 
138, 148 

motor of projector, 136-137 
piezoelectric projectors, 138-141, 147- 
148 

QB projectors, 144, 147 
quartz, 139-140 
roll and pitch, 64-65 
rotating, 213-214 


292 


INDEX 


sound output, 147-148 
sound source, 141-142 
transmission from deep water, 43 
transmission from shallow water, 
30-32 

voltage breakdown, 148 
Psychological characteristics of hearing, 
258-260 

Pulsed scanning sonar 
see Scanning sonar-pulsed trans- 
mission 

QB and QC projectors, 144, 147 
QGA projectors, 144, 147 
Quartz projectors, 139-140 

R sound rays, 27 

Radiation impedance of projectors, 
135-136 

Radiation in the ocean, 76 
back radiation, 76-77 
incoming radiation, 76 
Radio and Sound Laboratory, U. S. 
Navy, 44 

Radio sono buoy, anchored, 223 
Range calculation, echo ranging, 189- 
191, 196-199 

comparison of noise and reverbera- 
tion-limited ranges, 198-199 
comparison with listening range, 
267-268 

general principles, 189-190, 196-198 
maximum range, 190-191, 198-199 
noise-limited ranges, 189-191 
parameters, 190, 197-198 
ping length, 197-198 
recognition level for noise and rever- 
beration, 197 

reverberation-limited ranges, 196-199 
target speed and aspect, 164-165, 
169, 197 

Range calculation, listening, 266-272 
available signal output, 267 
comparison with echo ranging, 267- 
268 

critical band spectrum levels, 268-269 
equations and applications, 269-272 
maximum range, 268 
principles of range calculation, 267- 
268 

recognition level, 267 
Range indicator, sonar, 150 
Range recorder, echo ranging, 185-186 
Ranging on echoes 
see Echo ranging 

Rayleigh formula, reverberation, 85, 92 
RCG (reverberation controlled gain), 
220 

Receivers for listening gear 
see Hydrophones 
Recognition level 


listening, 267 

noise and reverberation, 197 
Recommendations for future research 
attenuation coefficient, 57 
low frequency transmission, 52 
roll and pitch of projector, 64 
scattering of sound, 33 
thermal microstructure in the sea, 34 
Reflection of sound 

effective reflection coefficient, 49-50 
formula for pressure, 45 
from large sphere, 113-114 
interference with direct signal, 24-25, 
36-37 

ocean bottom, 36-40, 45, 48-50, 59 
reverberation, 108, 110-111, 113-114 
surface reflection, 23-25, 45, 109-110 
time delay of reflected pulse, 23-24 
Refraction of sound, 10-21 
bottom reverberation, 110-111 
downward, effect on reverberation, 
108 

error in depth determination, 221 
image effect, 25, 46-48 
Snell’s law, 14 
sound ray diagrams, 15-16 
temperature variations in the sea, 
12-13 

theory, 14-15 
typical diagrams, 15-21 
velocity of sound, 10-11, 14 
Response curves of underwater sounds, 
222-223 

Reverberation, 82-114 
amplitude of reverberation, 91-95 
average reverberation curves, 104- 
106, 109 

beam-pattern correction, 90 
bottom reverberation, 88-90, 109-112 
coherence of reverberation, 93-95 
doppler effect, 180 
effect of ping length, 87-88, 92, 95 
effect of wind speed, 104-106 
forward scattering from ECR layer, 
112-113 

general discussion, 82 
hydrophones, 179-180 
in deep water, 99-114 
indices, 91 
level, 90-92, 111-112 
measurement of reverberation dis- 
tortion, 95-97 
oscillograms, 91, 94, 98 
pitch, 82 

Rayleigh formula, 85, 92 
recognition, 195 
recognition level, 197 
reflected sound, 108, 110-111, 113-114 
reverberation tail, 61, 112 
scattering by single particles, 83-87 
scattering coefficients, 90 


small object detection, 219 
spines of reverberation, 92 
surface reverberation, 88-90, 106-107 
theory, 87-98 

volume reverberation, 87-88, 99-104, 
107-109 

wave form, 95-98 

Reverberation, echo ranging, 195-199 
echo recognition, 195-196 
frequency, 192-193 
maximum echo ranges, 196-199 
ping length, 219-220 
spectrum of reverberation, 192-193 
Reverberation controlled gain (RCG), 
220 

Rochelle salt projectors, 140-141, 230 

SC rays (sound channel), 27 
Scanning sonar — continuous transmis- 
sion 

see FM scanning sonar 
Scanning sonar-pulsed transmission, 
210-214 

CR and ER sonar, 212-213 
echo duration, 211-212 
objective, 210 

plan position indicators, 212 
principles of operation, 210-212 
rotating projectors, 213-214 
sector scan sonar, 213 
Scattering of sound 
acoustic shadow, 33 
attenuation, 103 

coefficients, 90, 102-103, 107, 112 
definition, 55 

echo formation theory, 83-84 
echoes from small particles, 84-85 
effect of frequency, 85-86 
effective cross section, 84 
intensity, 84 
recommendations, 33 
reverberations, 83-87, 90, 100-103 
ship wakes, 123-125, 127-128 
target area, 85-87 
target strength, 84 
theory, 33 
transmission loss, 9 
travel time, 62 
Sea noise, 249-250 
Sector scan sonar, 213 
Shadow, acoustic 
see Acoustic shadow 
Ship sounds 

see Surface ship sounds 
Shock wave, 22 
Shrimp noise, 251-252 
Signal distortion, 60-62, 226 
Signal fluctuation, 62-66 

autocorrelation coefficient, 63-64 
causes, 47-48, 64-66 
deep projector, 44 


INDEX 


293 


definition, 60 

direct sound and surface echo, 65 
error in target strength measure- 
ment, 163-164 
measurement, 62-63 
roll and pitch of the projector, 64-65 
transmission loss, 60-66 
variance, 62 
Signal variation 
causes, 66-67 
definition, 60 

statistical treatment of data, 66-67 
transmission loss, 60 
Small object detection (SOD), 219-220 
echo-reverberation ratio, 219-220 
general principles, 219 
ping length, 219-220 
reverberation, 219 
Snell’s law of refraction, 14 
Sonar devices 

anchored radio sono buoy, 223 
bearing deviation indicator, 209-210 
expendable radio sono buoy, 223 
noise level monitor, 232 
own-doppler nullifier, 180 
phase-actuated locator, 207 
plan position indicator, 212-213 
range indicator, 150 
range recorder for echo ranging, 185- 
186 

reverberation controlled gain, 220 
small object detection, 219-220 
vector bearing indicator, 207 
Sonar projectors 
see Projectors, sonar 
Sonar systems 

CR and ER scanning sonar, 212-213 
FM scanning sonar, 214-219 
scanning sonar-pulsed transmission, 
210-214 

Sonic frequency transmission, 44-54 

7.5 kc sound, 52 

22.5 kc sound, 50-51 
comparison with supersonic, 44 
effect of range, 50 
experiments, 44-45 
hydrophone depth, 51-52 
ocean bottom reflection, 48-50 
simultaneous transmission of fre- 
quencies, 50-51 

sound paths, 48 
surface image effect, 45-48 
transmission loss, 274-275 
Sonic listening, noise background, 272- 
275 

ambient, 273 
directivity, 272-273 
equipment noise, 273 
reduction, 269-270 
sound output, 272 
Sono buoy, radio, 223 


Sound, psychological characteristics, 
258-260 

Sound, single-frequency components, 
239-242 

audibility, 239-240 
time patterns, 240-242 
Sound absorption 
air bubbles, 55 
causes, 55-57 
definition, 9, 55 
ship wakes, 123-125, 127-128 
viscosity, 57-58 
Sound attenuation 

see Attenuation of sound 
Sound channels 
definition, 17 

explosions in permanent channel, 
27-29 

Sound level, 1-2 
direct sound, 25-27 
echoes, 84, 154-158, 167-169 
effect of frequency, 237 
for typical ray diagrams, 17-20 
formula, 2 
overall level, 225 

ray divergence and intensity, 17-19 
scattered sound, 83 
submarine sounds, 232-234 
surface ships, 235 
underwater explosions, 25-27 
volume reverberation, 87-88 
wakes, 127-128 
Sound masking 

see Masking, auditory 
Sound measurement 

see Underwater sound measurement 
Sound peaks, 24 
Sound pressure, 1-2 
Sound ray diagrams, 15-21 

crossing rays and sound channels, 17 
isothermal layer and thermocline, 
16-17, 31 
limiting ra}' r , 16 

sharp downward refraction, 15-16 
sound intensity, 17-21, 26 
split-beam pattern, 16 
Sound ray theory, 14-15, 32-35 
attenuation coefficient, 34-36 
diffraction, 33 

formation of shadows, 16-17 
instrument for plotting rays, 15 
layer effect, 17, 21 
limiting range, 32-33 
rays in a composite gradient, 15 
rays in a constant gradient, 14-15 
scattering of sound, 33 
Snell’s law of refraction, 14 
supersonic frequency transmission, 
32-35 

thermal microstructure in sea, 33 
weak gradients, 34 


Sound reflection 

see Reflection of sound 
Sound refraction 

see Refraction of sound 
Sound scattering 

see Scattering of sound 
Sound spectrum 

see Spectrum of sound 
Sound transmission, ocean 

see Underwater sound transmission 
Sound travel time patterns, 237-242 
changes in spectrum, 239 
perception of time patterns, 238 
single-frequency components, 240- 
242 

Sound underwater 
see Underwater sound 
Sound velocity, underwater 
influencing factors, 10-11 
measurement, 13 

Specifications for hydrophones, 181-182 
Spectrum of sound 
circuit noise, 245 

critical band level, 262-263, 268-269 
energy level of pulse, 177-178 
fish noise, 252 
hydrophone level, 177-178 
level, spectrum, 225 
line spectrum, 226 
reverberation, 192-193 
sea noise, 249 
spectrograph, 239 
submarine sounds, 231, 233-234 
surface ships, 235-236 
Spines of reverberation, 92 
Spool pulse, 37 

Submarine sounds, 230-232, 247-248 
directivity, 234-235 
effect of speed, 248 
measurement, 231-232 
overall source levels, 232-234 
propeller beats, 231, 238 
sound spectra, 231, 233-234 
sources, 231 
Submarine wakes 
see Wakes of ships 

Submarines, target strength measure- 
ment, 165 

Supersonic frequency transmission, 29- 
44 

24 kc sound, 43-44 
60 kc sound, 42-43 
comparison of theory and experi- 
ment, 32-35 

comparison with sonic, 44 
deep water, 43-44 
depth of thermocline, 32 
echo ranging, 148-150 
experiments, 29-30 
influencing factors, 30-32 
isothermal layer, 31 


294 


INDEX 


negative surface gradients, 31 
ocean depth, 31-32, 39-40 
range, 31 

reflection from ocean bottom, 36-40 
shallow water, 30-32, 40-42 
Supersonic listening, 275-277 
available signal level, 276 
listening gear, 230 
recognition, 275-277 
transmission loss, 276 
Surface reverberation, 88-90, 106-107 
beam-pattern correction, 90 
dependence on wind speed, 107 
effect of range, 89, 104 
horizontally directed beam, 106-107 
scattering coefficient, 90, 107 
Surface ship sounds, 235-237 
cavitation, 237 

distribution of sound field, 237 
measurement, 235 
overall sound output, 235 
propeller beats, 238 
spectra of sounds, 235-237 
Surface vessel wakes 
see Wakes of ships 

Target area, 83-87 
effect on echoes, 83 
non-spherical objects, 86 
of bubbles, 85-86 
small scatterers, 85 
variation with sound wavelength, 84 
Target aspect, 164-169 
echo intensity, 167-169 
effect on echo range calculation, 198 
effect on echo shape, 165-167 
effect on target strength, 164-165 
measurement, 159 
Target bearing, 204-210 
bearing deviation, 205 
crossing the target, 205 
depth determination, 221 
maintaining contact, 205 
multiple hydrophones and split 
transducers, 205-207 
Target depth determination, 221 
Target detection, echo ranging, 201-204 
single ping, 201-202 
successive pings, 201-203 
Target doppler, 194 
Target search operations, 200-204 
effect of motion of sonar and target, 
202-204 

objectives, 200-201 
probability of target detection, 201- 
204 

Target strength, echo ranging, 153-165 
definition, 84, 153 
function of frequency, 169 
function of range and target speed, 
169 


function of target aspect, 164-165 
general principles, 153-154 
of spheres, 153-154 
scattered sound, 84 
submarines, 165 

Target strength measurement, 158-164 
acoustic experiments, 159-161 
echo and source level, 84, 162-163 
errors caused by fluctuation, 163-164 
method, 158 

optical experiments, 159-161 
ships and submarines, 161-164 
transmission loss, 163 
triplane, 174 

use of scaled models, 159-160 
Targets, artificial 
bubble targets, 174 
echo repeater, 153 
echoes, 170-174 

Temperature factors, ocean, 68-79 
afternoon effect, 75-76 
diurnal temperature cycle, 74-76 
heat budget of the ocean, 77 
heating and cooling, 71, 76-77 
mixing processes, 71-72, 77-78 
rotation of the earth, 78 
seasonal temperature changes, 74-75 
stability of ocean layers, 69-71 
stratification of the ocean, 69-71 
thermal structure at great depths, 
72-74 

transport by currents, 72, 78-79 
Temperature measuring instrument, 
ocean 

see Bathythermograph measure- 
ments 

Thermal gradients 

see also Negative gradients in the 
ocean 

attenuation coefficient, 58 
deep gradients, 41-42, 72-74 
positive, 71, 81 

recommendations for future re- 
search, 33-34 
stability, 69, 71 
transmission of sound, 55 
weak gradients, 34 
Thermocline layer 

attenuation coefficient, 34 
definition, 13 

effect of depth on transmission, 32 
sound ray diagrams, 16-17, 31 
Thresholds 
hearing, 258 
hydrophone, 180-181 
inherent threshold of sound, 227 



single-frequency components, 240- 
242 

Time-varied gain, 210, 220 
Train length of sound pulses, 87 
Transducers 

see Hydrophones; Projectors, sonar 
Transformer pulse, 37 
Transmission loss, 7-8, 60-67 
see also Scattering of sound 
autocorrelation, 63-64 
bottom reverberation, 109-110 
bottom-reflected sound, 274-275 
low frequencies, 274-275 
signal distortion, 60-62 
signal fluctuation, 60-66 
signal variation, 60 
supersonic listening, 275-277 
target strength measurement, 163 
temperature distribution, 29 
variability with time, 60, 66-67 
Transmission of sound in the sea 
see Underwater sound transmission 
Triplane, practice target, 170-174 
TVG control (time-varied gain), 210, 
220 

Ultrasonic frequency transmission 
see Supersonic frequency transmission 
Underwater explosions, 22-29 
compression wave, 23 
explosion bubble and its oscillation, 
22-23 

intensity of direct sound, 25-27 
permanent sound channel, 27-29 
reflection of sound at surface, 23-25 
refraction and image effect, 25 
sound in the acoustic shadow, 27 
summary of theory, 29 
Underwater projectors 
see Projectors, sonar 
Underwater sound anatysis, 223-241 
general description of sounds, 224-225 
listening to sounds, 223-224, 227-230 
single-frequency components, 239- 
242 

sounds of submarines, 230-232 
sounds of surface ships, 235-237 
time patterns and propeller beats, 
237-242 

Underwater sound measurement 

calibration of measuring systems, 224 
distortion, 226 
inherent threshold, 226 
measuring instruments, 224 
oscillograms, 226 
overall levels, 225 
response curves, 224-225 
spectrum level, 225 

Underwater sound transmission, 6-9, 
22-67 

absorption of sound, 9 


INDEX 


295 


acoustic properties of the ocean, 6-7 
attenuation of sound, 7, 9, 55-60 
hydrophone depth, 31-32, 43, 51-52 
ideal medium, 1-6 
image effect, 45-46 
ocean layer depth, 30, 39-40 
order of arrival of sounds, 28-29 
oscillograms, 60, 226 
recommendations for low frequen- 
cies, 52 

scattering of sound, 9 
shallow water, 30-32, 40-42 
sonic fequencies, 44-54 
supersonic horizontal beams, 29-44 
thermocline layer, 32 
through surface vessel wakes, 128-129 
transmission anomaly, 8-9 
transmission loss, 7-8, 60-67 
underwater explosions, 22-29 
U. S. Navy Radio and Sound Labora- 
tory, 44 

University of California 
ship wakes, 128 

sonic frequency transmission, 44 


supersonic frequency transmission, 
29-30 

Vector bearing indicator (VBI), 207 

Velocity of underwater sound 
influencing factors, 10-11 
measurement, 13 

Viscosity, sound absorption, 57-58 

Volume reverberation, 99-104, 107-109 
beam-pattern correction, 90 
deep scattering layers, 100-102 
dependence on frequency, 103-104 
dependence on range, 89, 99, 104 
dependence on wind speed, 107 
ECR layer, 108 
effect of attenuation, 108 
intensity, 87-88 

scattering coefficient, 90, 102-103 
with horizontal beam, 104-109 
with tilted beam, 99-104 

Wakes of ships, 115-132 
acoustic properties, 117-119 
age of wakes, 128-130 



bubbly wakes, 122, 126-127 
cavitation, 120-122 
echo formation, 120-122, 129, 170 
measurement of sound intensity, 127 
narrow wakes, 124-125 
scattering and absorption of sound, 
123-125, 127-128 
screening action, 124-125 
strength, 125-126, 128-132 
temperature effects, 117 
theory of acoustic properties, 119-128 
transmission of sound through wakes, 
128-129 

wide wakes, 125-126 
Woods Hole Oceanographic Institution 
cavitation, effect on wake echoes, 122 
variability of transmission loss, 22 

X-cut quartz crystals, 139-140 

Y-cut quartz crystals,, 138, 139 

Z-cut quartz crystals, 139 






















































































































































































































































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